Sousterrain revisited: there is a plan B

Having considered my earlier note on the design of a sousterrain for a month, I'm now going to rip it up and start again.

Reasons for not building in concrete

The first reason for not building in concrete is obvious. The embodied energy is huge. To present a largely-concrete sousterran as an energy efficient or 'green' building is hard to justify to me, to the planning authorities, or to anyone else. However, there are two other, pragmatically more compelling, reasons not to use concrete.

The first is that I have limited experience of using concrete, and that, once constructed, a concrete structure is very hard to modify.

The second is that to have any guarantees of the integrity of a concrete structure, the material has to be of a consistent mix and individual modules have to be poured and cured essentially in one operation – if part of a module is part-cured before another part is poured, you will have lines of weakness. That's not a problem if you use readimix. However, my proposed site is quite a long way from any road that a readymix truck could comfortably use, and I have no plans to construct such a road (nor can I afford to). And, even if I had such a road, it passes under electricity lines which do not in my opinion have safe clearance for something as high as a readymix truck.

Reasons for building in timber

Timber is in principle a sustainable resource. Its processing does not embody very high energy inputs. It locks up atmospheric carbon for the lifetime of the structure. As a building material, it's as green as it gets. Furthermore, it has other advantages. It is (relatively) light, strong, and easy to work. If you want to modify a wooden structure, it is generally easy to do so. Its disadvantage is a corollary of its advantages: it is bio-degradable. In the long run, it rots, losing structural integrity and releasing the captured carbon back to the atmosphere.

However, there is are ways of working around the rot problem. One with which I'm very familiar is epoxy encapsulation Done right, provided the encapsulation is not breeched and the epoxy is not exposed to sunlight, it prevents rot indefinitely. Of course epoxy is (at least at present) synthesised from fossil hydrocarbon. Furthermore it's at least conventional to use glass fibre as a reinforcing material in some parts of wood/epoxy structures, and in the case of the sousterran a layer of glass fibre cloth laid over the dome sections would help to prevent localised pressure points causing an encapsulation breech, while a tensile belt of glass fibre tape would prevent the dome spreading. However, the embodied energy represented by the epoxy and glass in a wood/epoxy composite structure is orders of magnitude less than that in concrete.

My original primary reason for not choosing timber is that if a structure is built underground and starts to rot, it seemed to me that it would be very hard to repair. But the truth is that this isn't going to be very far underground – a metre at most. In the event of problems, uncovering the problem area in order to repair it is not in fact a very big issue.

Lightweight structure

The original plan for the concrete structure was that it would be cast in components off site and then moved on-site for erection. In concrete this was somewhat implausible – individual components would weigh in tons, and would require specialist equipment to move. Boy Alex has such equipment, but even so it would require a substantial input of his time and equipment. But building in wood, it becomes much more practical. No component should weight more than at most 200Kg, meaning that it can be managed by a team of men and simple hoists. Building components off-site in the Void means that they can be built out of the weather, and consequently the encapsulated timber stays very dry.

Overburden

The problem with building a lightweight timber sousterran is that actually you can't. If burying to an average depth of 1 metre, the overburden is about 1.7 tons per square metre, or 42 tons per dome. I'm finding it hard to believe that I can engineer a structure which can handle that amount of mass. So while a turf roof certainly is possible, and an overall finished shape that looks natural probably is possible.

Temporary structures

One of the driving issues behind this note is this: before I have planning permission to build my permanent structure, I need to have somewhere to live. Furthermore, I'm now going to have very limited money – far too little to enable me to build my whole structure in one phase. I need a warm and weatherproof structure before next winter. I have considered buying a second-hand mobile home, or buying (or making) a yurt, or building a temporary cabin. Each of these would make a very considerable dent in my available funds. Why spend money on an essentially disposable structure, when I could spend it on part of my permanent structure?

The alternative is to build one dome of my permanent structure, and to add to it as funds become available. The problem is that it's going to take some time to get planning permission, that for a structure as radical as this anything which upsets the planners is going to make permission even harder to get, and that pre-empting planning permission is one well-known way to get planners' backs up.

However, if the structure is modular, and built of a (relatively) light material, it does not have to be initially erected in its final place. It could (with permission from my co-conspirators) even be erected temporarily inside the high-slat shed. Furthermore, building one dome early allows it to be treated as a prototype. In the process of building it, other, alternative ways of doing it better are bound to be learned.

A further advantage of having a prototype dome is that there is something physical to show to the planners and building regulations people, who are bound to be at least sceptical about the structure. Also, if they do insist on changes, only one dome needs to be changed.

Hybrid structure

Both this note and the previous one have essentially presented the concrete structure and the wooden structure as alternatives. It isn't necessarily so. Some degree of concrete foundation is likely to be necessary – even if it is only piles under the bases of the pillars. A pile-and-slab concrete foundation is also plausible.

Casting the pillars in concrete is relatively unproblematic – certainly very much easier than the flying buttresses or the domes. Building the walls in concrete blockwork is trivial (although it's easier to route services inside a wooden wall than inside a concrete one). Even the lintels joining the pillars are relatively simple to cast in concrete, whether they are cast in place or cast off-site.

So it would be entirely plausible to have a structure which was concrete with wooden domes, or concrete with wooden lintels and domes.

The flying buttresses in the original design then become an issue. With wooden domes having a tensile band, they aren't strictly necessary – the tensile band makes the dome self-supporting. But, sculpturally, I like them. They could be built in epoxy encapsulated timber; or they could be solid oak (which would be nice – a little expensive, but not dreadfully). Or they could be concrete. It's not a decision which needs to be made in a hurry.

Note that the hybrid structure doesn't work well with the idea with the idea of erecting the prototype dome off-site, and, for that reason, doesn't work well with the idea of getting a prototype dome up quickly to live in in the short term. However, if the pillars and walls of the prototype had to be sacrificed that is not necessarily a huge loss.

Plan B

So, plan B is as follows.

1. Start immediately (in March) to build one experimental dome in epoxy encapsulated timber with an intention to have it habitable by May
2. Erect that in a suitable place 'off site' (and not earth sheltered) until planning permission has been obtained.
3. When planning permission has been obtained, dig out the platform (the entire platform large enough for all four planned domes).
4. Lay suitable foundations for one dome.
5. Disassemble the prototype dome and re-erect it on-site.
6. Back-fill over that dome only, leaving the remainder of the platform clear.
7. Occupy that one dome, at least for winter 2011-2012; build other domes in a similar fashion at funds allow.

The joys of data transfer

OK, so, at this stage the main thing this blog is for is to find out how to import existing blog posts into Blogger. Brief summary: my existing blog uses a blogging engine I wrote myself back in 2000; it's quite a good blogging engine but it's not used by very many people because I didn't promote it enough back in the day, and so it's time to end-of-life it and migrate the existing users to something else.

Blogger has a mechanism for exporting and importing blogs. So, I thought, it ought to be possible to generate  the export format, which is documented here, from my existing data and then import that. From the documentation it was clear that the format was slightly bizarre - a well formed XML wrapper around data which is actually XML and presumably also well formed but is represented as text. However, I generated stuff that looked right to me according to the documentation, and it failed to import.

Worse, the error message given was terse to the point of unusability, and there's apparently no documentation of the error codes available on the web.

So the next thing to do was to export this blog from Blogger, and see whether the export file format looked anything like the documentation. And, guess what, it sort of doesn't. Which is to say that while the file format shown in the documentation is a very small subset of what's actually generated, it is such a noddy example that it doesn't even nearly represent what one needs to generate.

And, of course, there's no guarantee that even if I did succeeded in generating all the cruft that's in the format as generated by Blogger, I'd get my data to reimport - since the format includes magic identifiers which may represent objects in Google's persistent data space.

So it may be time to think of other ways to work around this.

End of eating dogfood

I wrote the Press Release System (PRES) back in 2000, and have kept my own blog on it since 2004. It wasn't a bad blogging engine. But I didn't promote it nearly enough, and very few people use it. So it no longer makes sense to maintain it - it's time to move to a more mainstream engine.

I can't help being slightly sad.

Site specific low cost housing for a windy site

Part of the issue of building housing on the site we're considering is the wind speed, which is high. I imagine we're all going to want homes which don't take a lot of energy to heat, and the wind-chill effect on exposed walls is going to be considerable. The parts of the site which are most exposed to the wind are also the sunniest – the southern and western slopes. Of course, one can insulate, and straw bales are worth considering.

However the alternative, given that we have reasonably steep slopes, is to get down out of the wind. And if you do that you also lessen the landscape impact of the dwelling dramatically.

We all need structures which are low cost and simple to erect (since we're likely to be using mostly our own labour).

My suggested response to this set of problems is to dig into the hillside, build structure, and backfill over it. The modules I'm suggesting are hexagonal, simply because I like the shapes sculpturally – cross vaults might be more practical, because you'd get a rectangular floor plan, but you'd also end up with straight lines on the hillside which would be more visually intrusive. One advantage of the hexagonal module is that you can put the modules together to follow the contour in a more flexible way. The approximate size of the module is 2.4 metres per side, or 4.8 metres diameter. This gives a floor area of 15 square metres (about 150 square feet) per module.

Note that I'm guessing that this structure would be low cost – I haven't had it costed by anyone remotely qualified to do so.

Sustainable?

This proposal is mainly concrete. I would have preferred timber but am not confident I can design in timber in a way that would be durable and maintainable under ground. As such there's a substantial energy cost in making the cement. There's also embodied energy in vermiculite used as filler. Overall, though, it isn't hugely much concrete – probably not as much per living unit as in a conventional block of flats. Because there's no wind exposure, and all the exposed sides are oriented towards the sun, it should have adequate passive heating even in winter; any supplementary space heating needed, water heating and cooking can be provided by a stove burning fuelwood grown on site. Large opening windows allow for cooling in summer.

Visual impact

One of the main objectives of this design is to minimise visual impact on the landscape. Because the terrace retaining wall is half the height of exposed sides of the structure, and because the slope above the structure matches the slope below the structure, from upslope or downslope there will be very little to see until you're very close.

From further away there will be a horizontal visible feature in the slope, but because all the curves are organic it shouldn't look too visually intrusive or artificial.

Elements

The building is constructed of four different concrete elements, as follows:

Dome segment

Obviously, six dome segments are needed for each dome. These will be the heaviest elements, and most difficult to move; it would be preferable to cast them in place, by erecting the pillars first and then erecting the former where the dome segment is to be located. Even if the segments are cast in place, however, they probably need to be separate segments rather than a single monolithic dome because of expansion issues. The cross section of the dome is probably a catenary, rather than an arc.

Pillar

One pillar at each corner of each dome, obviously. Hollow pillars – even if they do not contain drains – will be lighter and easier to install without being substantially weaker, so the core of the pillar element might be a spun concrete pipe section. The pillars need only be two metres tall because the natural shape of the edge of the dome will in any case form a slight arch.

Flying Buttress

Domes have thrust: they want to fall down, and in doing so they push out radially at their base. This thrust has to be resolved. In the unexposed edges of the dome (which, when building into the hillside, is most of them) that thrust is resolved simply by backfilling the soil. On the exposed edges – which we want, because we want light an air into the dwelling – the nature of hexagonal cells is that some corners are convex, and some are concave. How many of which you have depends on the shape of the site. On each convex corner you need something to take the thrust of the dome, and my choice it to have a flying buttress. This would span a terrace in front of the building and transfer load to its retaining wall.

Eve

The eve element is essentially just cosmetic; it joins adjacent flying buttress or eve elements into a continuous organic curve, again helping to reduce straight lines in the landscape. The eve units are designed so that although they show a fair curve on the outside they have a horizontal on the inside, so that ordinary standard patio door double glazed units can be used in all the exposed sides.

Building method

Again, this needs to be run past people with more experience than I have. Preventing damp ingress into the dwelling needs to be thought about carefully.

Dig back into the hillside

Strip off the turf and retain it. With a mechanical digger, dig back into the hillside; obviously, choose a site with contours which minimise the amount of digging that needs to be done. Reserve the soil removed, we'll need it later. Reserve topsoil separately from subsoil. The rock on site is part of the Kirkcudbright Shales and is probably soft enough to break up with a digger, is actual rock needs to be removed.

Lay drains

Lay drains under the site from uphill to downhill; these will later be joined to lateral collectors on the uphill side to reduce water pressure uphill. Rainwater drains can simply discharge downslope – they're only carrying water which would naturally drain down the slope anyway. A separate soil drain needs to lead to some suitable treatment.

Level platform

Level roughly with hardcore; finish with sand.

Pour slab

Taking one hexagonal module at a time, lay a waterproof membrane on the sand with at least 2.5 metres overlap on the uphill side, shutter the hexagon, and pour a self-levelling concrete. I need advice on the thickness of the slab. It almost certainly needs to be thicker under the pillars.

Erect pillars

It's possible that the pillars should be hollow with a drain down the centre of each one, linked into the under-slab drains, to move water from over the structure to under it. However, there's an issue about how to achieve a watertight seal at the top of these, so unless someone else can solve it that isn't part of the plan. In any case Pete suggests that the pillars should be founded on concrete piles going down to bedrock.

Erect uphill walls

Between each pair of pillars on sides which will be backfilled, erect a breeze block wall.

Erect terrace retaining wall

In front of the structure along edges that are to be exposed, erect a dry-stane dyke about a metre high and about two to three metres away from the structure, with footings in the right places for the flying buttresses. The exact width of the terrace at any point should be chosen so that when the structure is complete and backfilled, the slope above the building should continue as a fair curve in the slope below the building.

Part-backfill the uphill side

Bring the excess waterproof membrane laid down when pouring the slab up the sides of the newly erected uphill walls. Backfill, installing lateral drains as you go. At this stage, backfill to about 50cm below the tops of the walls.

Erect flying buttresses, eves and (possibly) lintel arches

In order to resolve the thrust on the domes, the flying buttresses and eves must be in place before the domes are cast – otherwise they'll just fall down as soon as the armature is removed. However, not all the pillars are supported against thrust in all the necessary directions until all the domes are up – to some extent, once completed the domes will support one another. One solution to this would be to cast lintels between each pair of adjacent pillars. If this solution is chosen, they must be installed at this stage. Alternative solutions are

• Embed a tensile steel reinforcing belt as low as possible in each dome;
• Construct separate armatures for each dome and leave them in place until all domes are cast and cured.

Erect domes

For each dome that is erected, a wooden armature needs to be erected to support the segments until all are in place. This armature needs to be supported on wedges so that when the dome is complete, the wedges can be driven out and the armature disassembled and moved to the next dome. Before the armature is removed, the flying buttress and eve elements which support the exposed edges of the structure must be installed.

Because of the steepness of the lower slopes of the dome, some though is needed on how to prevent the concrete from slumping before it is cured. Some upper surface shuttering may be required, and thought needs to be given to how to secure this. Also, it will probably be necessary to erect some sort of gantry or scaffold in order to apply and smooth concrete over the centres of the dome – because certainly that will be out of reach from the edges while the concrete is not set.

Fit chimney outer

Cut hole(s) for the chimney(s) in the appropriate place(s) in the domes (or, preferably, leave them when casting). Install vertical concrete pipe over the hole to the final ground level.

Fill valleys between the domes

On a settled, dry day, or better still on the first day of a run of settled dry days, fill the valleys between the domes with a lightweight inorganic filler material such as vermiculite. The object of this exercise is simply so that from every point on the structure, when the upper membrane is in place water will naturally drain to one edge and will not pool; the valleys do not have to be completely filled by any means. This doesn't need to be done if a watertight means of joining the upper membrane to drains running down internal pillars can be found.

Lay upper membrane

Lay a waterproof membrane over the whole structure, overlapping the uphill sides by half a metre. Fold this overlap down over the overlap of the lower membrane. Sealing around the chimney and any internal pillar drains is an issue I haven't solved, but I imagine suitable mastics may be available.

Backfill

Backfill over the whole structure, first with subsoil, then with topsoil. Contour the backfill to form a natural slope. Turf over. Similarly backfill against the retaining wall on the downslope side.

Install glazing

Ordinary standard double glazed 'patio door' units are installed into the exposed sides.

Fit out interior

To taste.

Rough costings

The following costings are preliminary, and are based on concrete costs only, with no allowance for levelling the platform, fitting drains, services, labour and so on; it's mainly to cost the bits of the structure I don't have a good feel for. This looks startlingly low – as if I've got something wrong by a factor of ten. I hope not!

Sousterran: quantities and mass
Concrete option							Cladding
Constants		Unit					Item			Unit	Price	per sq m
Mass of 1 cubic metre of concrete	2400	Kg					Bituthene 3000			20 metre roll	£163	£9.03
Mass of 1 cubic metre of soil	1700	Kg					Styrodur 3035CS, 30mm			14 sheets at 1250x600mm	£70	£6.67
Price of 1 cubic metre of concrete	100	Pounds sterling					Styrodur 3035CS, 60mm			7 sheets at 1250x600mm	£70	£13.33
Price of 1 8x4 sheet 15mm exterior ply	40	Pounds sterling					Total, with 30mm					£15.69
Price of 1 sq metre concrete blockwork	10	Pounds sterling					Total, with 60mm					£22.36
Dome radius (long axis)	2.4	metres
Area of dome floor	14.98	square metres
Area of dome surface	36.19	square metres
Number of wall panels	11	at	4.8	sq metres
Elements	Area sq m	Thickness m	Volume cu m	Mass tons	Concrete Cost	Cladding cost	Number of	Total cost	Total mass	Shuttering sheets	Shuttering cost
Floor	104.83	0.1	10.48	25.16	£1,048	£399	1	£1,448	25.16	1	£40
Dome	36.19	0.1	3.62	8.69	£362	£809	4	£4,685	34.74	42	£1,680
Dome segment	6.03	0.1	0.6	1.45	£60		24		34.74	7
Pillar			0.5	1.2	£50		17	£850	20.4	6	£240
Eve			1	2.4	£100		5	£500	12	4	£160
Flying buttress			2	4.8	£200		4	£800	19.2	6	£240
Wall	4.8	0.1	0.48	1.15	£48	£75	11	£1,357	12.67	0
Overburden	104.83	0.2	20.97	35.64	£0		1	£0	35.64	0	£0
Subtotals							50	£9,639	194.56		£2,360
Total, cost											£11,999

Practicalities of 'affordable' housing

This document attempts to address how in practice we would implement an affordable housing policy if we choose to do so.

The company – that is to say us together as a corporate entity – will buy the farm and resell the land to each of us; in reselling the land it can add a burden. But that would be a burden on the land, not on the dwellings, and I don't think that's what we want. We could probably sell the land with a condition of sale that any dwellings built on it would be subject to the burden, but I'm not certain exactly how we're do this – we need to check with a lawyer.

Rural housing burden

A particular form of burden that is available to us is the 'rural housing burden', established in section 43 of the Title Conditions (Scotland) Act 2003¹. To use this we'd have either to apply for the company to be registered as a 'rural housing body' or to work with an organisation already designated as a 'rural housing body'. It would be better if at all possible if we were registered.

The rural housing burden gives the 'rural housing body' – that is, the Standing Stone company – a right of pre-emption; which means, as I understand it, that the company has 42 days from the day you decide to sell to decide whether it will buy. Remember that the company is essentially just ourselves, taking decisions on a one member one vote basis; we could give the company in its constitution (memorandum and articles) a clause which says that a decision to buy a dwelling requires a general meeting, not just a decision by directors.

Under section 84 of the act, if the company does not decide to buy within 42 days, the 'rural housing burden' is automatically extinguished, and you can sell your dwelling on the open market.

I'm not clear from my reading of the act whether the company would have the right to pre-empt at a particular price (the 'just price' or 'affordable price' as discussed in my previous document); we might need an additional legal agreement to assert this – if that's what we want to do.

To what should the burden apply?

We've discussed in meetings the undesirability of people building a dwelling on a holding, then selling the dwelling and land separately, allowing someone to build a new dwelling on the remainder of the land, and so on, until we have a housing estate.

There are clearly two options:

1. The burden could apply to the dwelling and curtilage only
2. The burden could apply to the holding

But we need to be aware that people may want to sell parcels of land rather than their whole holding, and, within the context of company, we almost certainly want to allow that. If we don't apply the burden to the whole holding, we can't prevent people selling parcels of land to surrounding landowners, and we might want strongly not to allow that!

I'm not clear from the act whether a 'rural housing burden' can apply to a whole croft, or only to the dwelling; that's another thing we need to clarify.

Can we use other burdens?

The whole purpose of the 2003 act seems to be to limit the burdens that can be placed on housing. Very few are allowed. There is a form of burden called a 'community burden', but its purpose seems to be limited to the appointment of a managing agent, for example for a block of flats. A community burden does not appear to give the right to pre-empt a sale. So it seems to me that the rural housing burden is the only burden we can use.

Alternative price cap models

I can envisage four mechanisms for establishing a price at which the company can pre-empt a sale.

Land

It does not seem to me that it makes sense to apply a cap to the price of the land part of the holding. All land is to some extent subject to speculative pricing, and in particular the price of agricultural land is artificially inflated by public subsidies to farming, but there's little we can do about that: land has a commercial value, and an incoming holder can in principal try to make a commercial return on it – if they choose. So it seems sensible simply for the company to have the land valued as commercial agricultural land, and then pay that amount for the land element of the holding.

The existing farmhouse

It isn't reasonable to apply any price cap formula with the possible exception the 'just price' to the existing farmhouse. Ruth and Gav will have to pay the open market rate for the house (unless we jointly decide to subsidise her, which is possible but hasn't been discussed); having paid the open marked rate, it isn't fair to expect her to resell at a capped rate.

If we were to bring Ruth and Gav into the capped rate scheme, we would have to lower the price they pay for the farmhouse to £105,000 – which means that the ten other holdings would each have to put £3,500 into subsidising Ruth and Gav. That isn't impossible and would make things feel fairer in the long run, since everyone would then be subject to the same cap – but it adds complexity and is yet another thing to discuss and get right, and we have limited time.

The remainder of this discussion applies to the dwelling part of the holding, for new build dwellings.

Match price

The first model would be that the seller seeks a buyer on the open market and agrees a price; the company then has the right to match that price. I can see no advantage to the company in this; it would effectively mean allowing the price to rip with the speculative rise in house prices generally, and the company would in effect only be able to purchase properties if it could attract wealthy new members. I don't believe this is what we want.

'Affordable' price

The affordable price model uses a function simply based on local average wages to establish the price of a dwelling, without taking into account the actual amount of effort that has gone into that dwelling, or how well designed, spacious or well built it is. Of course, the 'affordable price' would be literally a ceiling, but in practice I think it would be very hard for the company to offer less than the ceiling price to a member wishing to sell.

This means that a member who had worked very hard to create a really nice house would get exactly the same price as someone who had done the minimum to get past building warrant, which seems a little unfair; but it's worth bearing in mind that the 'affordable' price is still likely to be higher than the 'just' price, since we're none of us very rich and therefore the 'just' price is likely in almost all cases to end up below the affordable price.

'Just' price

As I outlined in my previous document, the 'just' price seeks to represent what has actually been invested – including sweat equity, investment of your own labour – with an adjustment for inflation, so you can always get out the inflation-adjusted amount you put in. This is my preferred model, because it seems to me fairer – but it has a number of problems, and, essentially, it's only fairer if we're all honest. If a person claims a lot more 'sweat equity' hours than he or she has actually put in, the 'just' price is inflated. Also, keeping an accounting of what has been truly been invested in bought materials is also an issue, and could be manipulated.

'Reasonable cost' price

The 'reasonable cost' price is the price I described in 'just price revisited' in my previous document. It uses a formula based on the floor area of the dwelling in square metres, multiplied by an arbitrary assumed cost per square metre for which a dwelling could be built. This means that if you use marble staircases and solid gold taps, the 'reasonable cost' price will be lower than the 'just' price, and you may not recover your costs.

But, provided we agree a reasonable assumed cost – £1,200 seems a commonly cited value – then the 'reasonable cost' price will for most of us be about the same as or higher than the 'just' price.

Hybrid schemes

Note, of course, that to get the political support I believe we need in order to get planning permission, it will be greatly to our advantage to be able to talk about 'affordable price'. To do this, we could simply accept the 'affordable' price – which is likely to allow us all to make a significant profit. Or we could chose to use a hybrid scheme which said, for example, that the company will buy at either the 'affordable' price of the 'reasonable cost' price, whichever is the lower.

The 42 day rule

The 42 day rule is in the legislation and we can't vary it. Given that if the company fails to agree to buy within 42 days of being notified that the holding is for sale the burden ceases, we need to make an effort to ensure the company can buy – which means, we need to keep a register of people who are seriously interested in becoming members (and whom we would welcome as members).

What should never happen – and we should write a clause into the memorandum and articles to prevent this happening – is that the company buy someone's holding at the capped value and then sell it at the open market value. The company must resell for the amount for which it bought, with some allowance for fees. Obviously, in most cases it will probably be best for the company to allow the seller to sell to the new member directly, but at the price at which the company could pre-empt.

1http://www.legislation.gov.uk/asp/2003/9/section/43

A Just Price for housing

Standing Stone: reasons for adopting a 'just price' for housing

We live in a late capitalist society in which democratic politicians have deliberately stoked a speculative bubble in housing prices, because most voters are property owners and spiralling house prices mean that those who are already on the housing ladder feel richer. The consequence of this is that, over the country as a whole, house prices are already beyond the reach of many folk on ordinary wages. Along the Solway coast, the pretty villages have a price premium because they are attractive and pleasant places to live, but local wages are depressed. This means that folk working in the local economy cannot buy houses locally – unless they have inherited wealth.

So begins a process of clearance which is just as socially corrosive as the clearances of the eighteenth century, when the landowners enclosed land which had traditionally been common. The reaction, then, here in Galloway, was of a violent revolt by the country folk, throwing down the walls of the new enclosures and burning barns. Now, here in Auchencairn, I think the Caldows and Helen Sankey are the only people born in the village who still live on the main street (Geordie Milligan lives on Spout Row). Every other house is owned by incomers, and the native population has been effectively cleared across the burn into the bantustan of social housing. We have a very nearly complete ethnic segregation, with those who live in the old village now overwhelmingly rich and English, and the Crescent overwhelmingly poor and Scots.

It wasn't always like this. The three houses across the street for me, when last sold in the 1950s, were bought for less than two hundred and fifty pounds for all three. When I bought my first flat in the village, I paid four thousand pounds. Now, the only property for sale in the village under a hundred thousand pounds is Monty's flat – which is tiny.

Unless ordinary people without inherited wealth are able to afford to own houses in this area on wages earned in this area, the social dislocation and, effectively, ethnic cleansing is only going to get worse. Ultimately, that must lead to unrest.

Applying this to Standing Stone

None of this is the fault of anyone in the Standing Stone project. It is a consequence of political and economic forces which are far bigger than us.

However, if we do get planning permission to build new dwellings on the Standing Stone site, the market value of those dwellings when they are complete will be very much greater than what they cost to build. If we don't cap the resale price, then we are effectively giving one another a speculators' charter, and we risk the site rapidly developing into yet another rich incomers' enclave. We risk this both because the speculative opportunity will suck in spivs, and because your actual people – the sort of folk we would choose to live among, that we think in developing the idea that we are choosing to live among – simply won't be able to afford to buy into it.

People have objected – very reasonably – that they need to be able to get their investment out again. And it is true that if the housing market continues to spiral madly out of control, then if we put a cap on resale prices of dwellings at Standing Stone then people may not be able to leave, because the capped price will not realise enough money to buy a replacement property on the open market. These are real and reasonable issues.

The just price

Clearly if we are to derive a formula for a 'just price' for a dwelling, that formula needs to represent the investment which has been put in – including investment as 'sweat equity', our own labour which we've expended in creating the dwelling.

Furthermore, we need to notionally detach the value of the land from the value of the dwelling. The 'croft' part of the holding – without planning permission – has a value as agricultural land. So the capped value of a holding, if we choose to adopt a 'just price' cap, is the market value of the agricultural land plus the capped value of the dwelling, and (irrespective of what DGSHT's policy says) clearly the 'just price' cannot be less than the total amount reasonably invested. If Ruth has invested a sum in the farmhouse, then she must be able to realise at least that sum if at some time in the future she needs to sell. To expect her to accept less is just unreasonable.

But at the other end of the scale I'm expecting to spend less than £40,000 cash (and a lot of work) on structure. My dwelling, at the end of that, will have one bedroom, rather than the three or four that the farmhouse has, but as a modern designer structure with a nice view it's open market value isn't going to be a lot less. If I'm spending £55,000 on ten acres of land, then the pro-rata cost of the half-acre of that which forms the curtilage of the dwelling is about £2,500. For simplicity say I spend £7,500 on design fees and contractors, and value six months of my full-time equivalent labour at £10,000, then the investment cost of my dwelling is

Land:	£2,500
Fees and contractors	£7,500
Sweat equity	£10,000
Structure	£40,000
Total	£60,000

Should I be allowed to sell this dwelling which has cost me £60,000 for £120,000? Why? What justifies me making such a speculative profit?

The affordable price

The average annual wage in Dumfries and Galloway is around £20,000. This means that the cost price of my one bedroom dwelling is three times the income of a single wage earner – a multiplier which is certainly acceptable to mortgage lenders. Actually, DGSCHT consider a multiplier of 3.5 times average annual wage to be reasonable. And on a two bedroom dwelling, that's 3.5 times not the income of one wage earner, but the income of 1.5 wage earners – a household with one person working full time and one person working part time. So the affordable price of my one-bedroom dwelling would be £75,000, and the affordable price of a two or three bedroom dwelling would be £105,000.

Now, OK, in aiming for a £40,000 structure cost I'm aiming to build a structure which is affordable to me, so it has to be 'affordable' – I'm too old to take on new debt. But a cost of £1,200 per square metre seems a commonly quoted value these days, so (allowing the same figures for land value of the curtilage and for fees as in my example) you have £95,000 to spend on structure of two to three bedrooms (including sweat equity), which builds you 80 square metres of reasonable quality structure, which is equivalent to six rooms each 12 foot by 12 foot.

Thus it seems to me that it is possible to build new dwellings on the site such that the cost is lower than the 'affordable price'. Furthermore, knowing what I do of the group, all of us are going to have to build dwellings which cost less than the 'affordable price', simply because none of us are rich.

The just price revisited

This doesn't solve the Ruth conundrum, of course, because she's having to buy at full market rate and cannot be expected to take a hit to sell at an 'affordable price'.

So we need a formula which I think is something like this:

value of the land part of the holding

plus reasonable investment cost of dwelling

plus 2% per annum compound interest on the reasonable investment cost of the dwelling

where:

value of the land is the agricultural value of the land as assessed by a qualified surveyor appointed by the Company

reasonable investment cost is for new builds and for the byre units an agreed multiple on the internal area of the dwelling in square metres, I'd suggest £1,200; for the existing dwelling, the price actually paid (including essential renovations).

This gives us a 'just price' which for all new units is likely to be lower than or equal to the 'affordable price' as seen by DGSCHT.

Non-idealistic argument for a just price formula

The arguments I advanced at the head of this document for a just price for housing are idealistic; they represent a rejection of the market in favour of enhancing social cohesion and abstract 'fairness'. I believe that most of us do have a degree of idealism, but I acknowledge that the exact degree varies.

However, bear in mind that getting planning permission for ten new dwellings on this site is a very big ask. It is precisely the 'sporadic development in the countryside' that the council has policy to prevent. We're going to have to do a lot of special pleading and special argument. If we fail to get planning permission, we're most of us going to have had a significant share of all our capital tied up for at least two years in land, with nowhere to live. And although it's probable that if it all goes pear shaped we can resell the land for the money invested, that isn't guaranteed.

So we need all the help we can get. We can get a certain amount of political if we're able to play the 'green' card, the 'low impact' card (but I'm not certain I can achieve low impact in my budget, and I suspect other people may be the same; concrete is cheap stuff). One card that we know we can play, though, is 'affordable housing'. And, we already know that if we play the affordable housing card, we will get not insignificant help from DGSCHT.

In summary, if we cap resale at an 'affordable' value, we will be able to recover the investment made in dwellings (provided we're don't built using solid gold taps and marble staircases), and we will get significant support which will significantly lower the risk involved in the project. That seems to me a substantial win for very little actual cost.

Auf Essen in Deutschland

I've spent the week in Germany, where I've been performing a safety audit on a device made by a German subsidiary of a Swiss company on behalf of an English subsidiary of a French company. I write this sitting in France, fifty metres from Switzerland, while waiting for a plane to fly me to the Netherlands and thence home to Scotland. It's all remarkably painless.

But let's talk about Germany. Lots of the things you thought you knew (or I thought I knew) about Germany turn out to be true - or at least, turn out to be true of small towns on the fringes of the Schwartzwald. My view might be slightly influenced by the company I was auditing, by the fact that that Swiss-owned engineering company was absolutely obsessive about quality in everything they did (including hospitality). It was engineering of the kind I associate with Germany: always up to a quality, never down to a price. Over-engineered rather than under-engineered; good and thoughtful design, but emphasising sturdiness and durability over style.

The taxis were spotlessly clean, their drivers unfailingly courteous. The factory was clean and efficient and all the staff positive, relaxed, confident and happy to explain their work. The hotel was extremely well fitted and comfortable (and clean), the rooms generous and luxurious, the staff helpful, friendly and welcoming. They were mostly middle aged, not young; I think almost entirely local; and the ratio of staff to guests higher than you'd find in anything but the most upmarket British hotel. Yet the cost of a room was exactly the same as in a grubby corporate flea-pit in East Kilbride - where you would not have got the delicious and varied breakfast.

Which brings me to food. The company we were auditing treated us as guests; not only did they provide us with restaurant-quality lunch each day in their staff canteen, they took us out to dine every night, at a total of three different restaurants; twice the one belonging to our hotel, once a modern restaurant in the local administrative centre, and once... I'll come to that.

So what is German food like? Sausages and sourkraut? Chips and cream-cakes? Errr... no. We did eat a little sourkraut - several varieties of it, all good. We ate noodles, of kinds I'd never heard of before, let alone seen - nothing like Italian noodles. We ate dumplings. We once ate chips - once. We ate a simply extraordinary quantity of meat. We ate home made icecream. I didn't eat sausage at all (although a number of varieties were available at breakfast). Slightly to my disappointment I didn't eat a proper Schwartzwald Kirsche Torte - I could have, but I simply didn't have room (my abstemiousness at breakfast was for the same reason). I have eaten more this week than I eat in an average fortnight.

So, what is the food like? In one word, delicious. Extraordinarily good. Exceptional. Second, in my experience, only to Malaysia. Everything was of superb quality, freshly prepared, not over fancy. The effete over-complicated confections of British television cooking were nowhere to be seen; nor was fast food, or junk food. In the urban centres we did see a few Indian, Chinese and Vietnamese restaurants, and we did see sausageinnabun shops. But the places we went to served food which was proudly local, unashamedly German, unquestionably fresh-cooked and utterly excellent.

Until the very last night - last night - which was completely different. We drove up into the forest, up steeply climbing twisting roads which would be a joy to cycle in summer, to an ancient farm-house turned gasthof. The whole place was wooden, over four hundred years old. We went into a simple, homely dining room which would hold twenty people at the most, but which was empty but for a man sitting alone and the four of us. A pretty young waitress who spoke no English brought us simple paper menus, and came back after a few minutes to take our order. I chose a venison ragout with noodles, which sounded good.

So much, so normal. And then it all changed.

Mien host came in, a tall and powerful old man called Saxo, wearing casual countryman's clothes. He spoke a little English but was much more comfortable in German. He sat down with us for a few minutes, talking, and then said he'd shot a wild pig, and would we like some? After not a lot of discussion, we agreed we would. Was it spit-roasted, someone asked? No, it had been baked in the oven, after the bread he'd be serving with it. Saxo also said he had some mead, would we like to taste?

He disappeared into the back, and shortly reappeared bearing an enormous ox horn in a wrought iron stand. I joked that it must be an aurochs horn, but in truth I don't know where he got one so big; it wasn't old, and was by far bigger the horn of any domestic breed I know of except perhaps a Texas long-horn. He offered this to us and I realised it was full of mead. How much mead fills a horn like that? I haven't a clue, but it must have been at least two litres. I was certain that between four of us - and one a driver - we'd never empty it. So we chatted round the table with Saxo, and drank his (wonderful) mead, passing this epic horn from hand to hand, until the chef appeared.

The chef was a man as big as Saxo, and with the sort of belly on him a good chef should have. He greeted us, spoke to Saxo, and they both disappeared into the back. After a few moments they reappeared, bearing a trencher. A trencher? it was at least four feet by two, of sturdy oak. It filled the table, clearly leaving no room for such effete nonsense as individual plates. On it. besides two baked quarters of a substantial pig and a large loaf of rough bread cut into thick slices, were two large crocks of gravy, baked apples, baked potatoes, sweet corn, and a mountain of roughly chopped mushrooms (which, it transpired, were the only ingredient which had been bought in). Oh - and four very sharp knives. No forks.

Four people - four people could not possibly eat all this.

Four people very nearly did. There were some potatoes left at the end, and an apple, and perhaps a kilo of pork on the shoulder. We gorged ourselves. We all gorged ourselves, despite having already overeaten for three days, because it was so extraordinarily delicious, so utterly delectable.

And when, finally, we thought we had eaten all we possibly could and the trencher had been removed, the pretty waitress (who, it transpired, was not German but from Drakula's home village in Transylvania) persuaded us all to have some home-made ice-cream with advocaat; and Saxo reappeared and persuaded us to have a schnapps. The waitress and the other guest (an engineer from Bratislava in Slovakia) joined us, and together we conversed in a happy mixture of German, English, French, a bit of Italian, a bit of Dutch, and some Slovak, while the mead horn continued to circulate.

We could have had that meal - in that place, in that environment - any time in the past four hundred years; there was an electric light but it was no brighter or more intrusive than a candle lamp. Apart from the potatoes and sweet corn, we could have had it any time in the past millenium.

At the end of it all we went back to the hotel very late. I was drunker than I've been in twenty years - and probably happier. The mead horn? It was empty.

Settling a game world

This essay is part of a series with 'Worlds andFlats' and 'The spread of knowledge in a large gameworld'; if you haven't read those you may want to read them before reading this. This essay describes how a large world can come into being and can evolve. I've written again on this subject since - see 'Populating a game world')

Microworld

Some twenty years ago I wrote a rather sophisticated cellular automaton which I called 'Microworld' which modelled the spread of human population over a landscape. It did this by first fractally folding a grid to assign elevations to cells. Then, cells below a critical elevation – the tree line – were assigned as forest. For each cycle – 'year' – a cell remained forest, its soil fertility would increase. Random events – 'lightning strikes' could change a cell from forest to clearing. Then the following transitions might take place, each with a probability, where each cell is considered to have eight neighbours:

• A forest cell with a lightning strike as a neighbour may catch fire and burn
• A forest cell with a fire as a neighbour may catch fire and burn
• A burning cell become a clearing cell
• A clearing cell with forest or scrub as a neighbour may become scrub
• A scrub cell may become forest

This more or less completes the 'natural' cycle... then we get to settlement. Pastoral and agrarian 1 cells gradually degrade soil fertility (erosion, etc). Agrarian 2 cells do not degrade fertility.

• A clearing cell (including cells above the treeline) may become a pastoral cell (pastoral 1, no settlement)
• A pastoral 1 cell whose soil fertility falls below a threshhold becomes waste
• A pastoral 1 cell with no pastoral neighbours may become waste
• A waste cell below the treeline may become scrub
• A waste cell may become clearing
• A pastoral 1 cell with two or more pastoral neighbours may become a pastoral 2 cell (settlement)
• A forest cell with two or more pastoral neighbours may become clearing
• A pastoral 2 cell with two or more pastoral 2 neighbours may become agrarian 1
• An agrarian 1 cell which falls below a critical fertility becomes pastoral 1
• An agrarian 1 cell with three or more agrarian 1 neighbours becomes agrarian 2 (smith, mill)
• A cell with three or more agrarian 2 neighbours becomes market
• A market cell with no agrarian 2, market or urban neighbours becomes waste
• A cell with two or more market neighbours becomes urban

That's simple, but it provides a remarkable good model of population spread. however, it is essentially a grid and so doesn't make for natural-seeming landscapes when considered as a three dimensional rendered world. How can we do better?

Microworld Two

The objective of this essay is to outline an angorithm for creating inhabited landscapes in which games can be set, which are satisfyingly believable when rendered in three dimensions. The objective of creating landscapes 'procedurally' – that is, with algorithms – is that they can be very much larger than designed landscapes for the same richness of local detail. This does not mean that every aspect of the final landscape must be 'procedural'. It would be possible to use the techniques outlined here to create landscapes which were different every time the game was played, but it would be equally possible to create a landscape which was frozen at a particular point and then hand edited to add features useful to the game's plot. And while I'm principally thinking in this about role playing games, this sort of landscape would be applicable to many other sorts of games – strategy games, god games, first person shooters...

The physical geography

Consider our landscape as, once again, a fractally folded sheet on which any given point has characteristics based on its elevation and orientation. There are two critical levels – water level and treeline. The water level is, overall, sea level, but in the case of a localised depression it is equal to the lowest land height between the depression and the sea (lakes form in depressions). Computing the fractal sheet forms stage one in computing the landscape. Next, we need functions which, for any given point on the landscape, compute two different dimensions of soil fertility: water and warmth. We'll assume a coriolis prevailing wind blowing from the west, bringing in damp air from an ocean in that direction. Western slopes are wetter than eastern slopes. In principle, also, there's likely to be a rain shadow to the east of high ground leading to considerable aridity, but that may be too expensive to compute. Rain runs swiftly off steeper slopes, more slowly on flatter ground, so flatter ground is wetter than steeper ground. Water flows down hill, so lower ground is on the whole wetter than higher ground. This isn't a precise model of soil hydrology, but I think it's good enough. From each lake a watercourse follows the lowest possible path to the sea. Watercourses modify the land overwhich they flow, carving out a route at least sufficient to carry the amount of water collected in the watershed above each point. Where watercourses flow down steeper gradients, they carve out gullies, possibly with waterfalls. Where they cross shallower gradients or level ground, they become broader. Computing the watercourses becomes the second stage of computing the lanscape.

Vegetation

Now sprinkle seeds randomly across the landscape at a density of roughly one every ten square metres. Seeds which fall in water, ignore (? or make into water plants?). The position of the plant is taken from the random sprinkling. The species and size of the plant that grows from the plant are a function of the water and warmth functions described above, with latitude and longitude as seeds for pseudo-random functions delivering aspects like branching and so on – enough to make individual plants distinct and not carbon copies even of other plants of the same species, but nevertheless recreatable from just the latitude and longitude. So for each plant only two integers need to be stored, yet every time a player passes he will see an identically recreated world. Of course there is a trade-off between storage space and rendering time, and it may be more efficient to build and cache a detailed model of each plant. Like a lot of other things it depends on the game being designed and the processing power of the platform on which that game is delivered. As to how the functions which select the vegetation type work, obviously trees grow better in wetter places, grassland plants in dryer places; within the wetter places, coniferous trees are more prevalent where it is cooler, broadleaves where it is warmer. In the very wettest places, willows, alders and marshland plants. These plants – the seeded plants – are the feature plants of the landscape. When rendering the landscape the renderer would first apply a suitable local surface texture, for example, in grassland areas, grass.

Settling the world

So now we need to make this an inhabited landscape. My proposal for this is to introduce proto-actors, which may be the same software agents as the non-player characters the user will interact with (see my essay on the spread of knowledge). At this stage in their lifecycle, the proto-actors are fairly simple state transition machines. Generally, their algorithm is as follows: Starting from one or two seed points, proto-agents will initially move across the landscape travelling at most 20Km in a day, preferring to stop at inns or else at existing settlements; and will maintain a history of the places they have been, never revisiting a place until they have settled. Whenever moving, whether before they have settled or after, proto-actors will plan their route across the landscape, avoiding trees, buildings, and steep gradients, and will prefer to cross rivers at a bridge (if available) or else a ferry (if available), or failing that at the narrowest convenient point. When proto-actors settle, they will claim an area of territory appropriate to their trade – more below; the system must build up a database of land holdings. In particular a land holding will never cross a watercourse, an existing road or overlap another land holding (although roads may develop across existing holdings). This is key because I don't want holdings normally to have regular shapes. A settled proto-agent will build a building to live in, and possibly an additional one for his trade. When building buildings, proto-actors will prefer to build at the edge of their land holding, as close as possible to existing buildings and ideally at the side of an existing road. The richer an existing building is, the more attractive it will be to new buildings. Buildings will be built with their long edge aligned with the edge of the owner's hoding.

• A proto-actor is initially, as described above, an itinerant. Itinerants are introduced into the world at a small number of geographical locations, and gradually, not all at once. Itinerants travel as described above. As they move they will leave breadcrumb trails with a roughly ten metre resolution. If they cross an existing track which goes in roughly the right direction they will prefer to follow it. Once a track has been followed by a certain number of proto-actors, it becomes a road.
• An itinerant who finds an area of unsettled grassland of ten hectares with low soil fertility and not more than one hundred trees settles and becomes a pastoralist. He builds a cottage.
• An itinerant who finds an area of unsettled grassland of ten hectares with medium or high soil fertility becomes an agrarian. He builds a homestead. Depending on the fertility of his land he can support between zero and ten labourers, 10% of a smith, 10% of a miller and 10% of a bonnet laird.
• An itinerant who finds an area of unsettled land of 100 square metres within five hundred metres of a homestead with unfulfilled labourer demand becomes a labourer. He builds a cottage.
• An itinerant who finds an area of unsettled land of 100 square metres within five kilometres of ten farmers with unfilled smithing slots becomes a smith. He builds a cottage and a forge.
• An itinerant who finds an area of unsettled land either at the side of a water course or at the top of a hill, and within 5 kilometers of ten farmers with unfilled milling slots becomes a miller. He builds a mill – water or wind, appropriate to location.
• Any settler who plays host to more than a certain number of travellers becomes an innkeeper. He claims 400 square metres of unclaimed land as close as possible to his existing settlement and buids an inn and stableyard.
• An itinerant who finds 400 square metres of unclaimed land within a certain distance of an inn and a smith will become a merchant, provided that there are three smiths within a 5Km radius who have unfilled market slots. The merchant builds a marketplace and a counting house.
• An itinerant who finds 200 square metres of unclaimed land within a specified distance of a market with an unfilled chapel slot becomes a priest and builds a chapel and manse, and possibly a school.
• An itinerant who finds 100 square metres of unclaimed land adjacent to where a road crosses a river becomes a ferryman.
• A ferryman who carries more than a certain number of passengers in a given period becomes a tollkeeper and builds a bridge.

This set of rules – and possibly others like them (woodcutters, fishermen, hunters...) provide the first wave of settlement. Once the landscape is sufficiently settled by this first wave, there needs to be a period of establishing trading routes. First, every settler will visit his nearest market, leaving a permanent track if there is not already a road. Where several of these tracks overlay one another, once again a road is created. Each merchant then visits each of the ten markets nearest his own, following existing tracks and roads where available. Wherever the merchants do not find roads, new roads are created. This completes the roads network. Each market is now assigned a value which is a function of

• the number of people for whom it is the nearest market
• the sum of the wealth (soil fertility) of the homesteads for which it is the nearest market
• the wealth of other markets within a day's travel

Depending on its wealth a market may support up to twenty stallholders, including bakers, butchers, tanners, weavers, cobblers, chandlers and so on. So a second wave of itinerants sets off. These follow the original rules for itinerants, but if they find an unsettled 100 square metres within five hundred metres of a market, will set up as a stallholder, building a town house and appropriate trade building on their own settlement, and a stall in the market. An itinerant finding a hundred square metres within five hundred metres of a market which has all its stallholder slots filled may become a slum landlord, and build a tenement for day-labourers. Finally, aristocracy. In the second wave an itinerant who finds either a hilltop, an island in a lake or river, or a significant river crossing, with one hectare of unclaimed land and within 5Km of ten farms with unfilled bonnet laird slots becomes a bonnet laird (or 'squire', if you prefer) and builds a fortified house. At the end of the second wave of settlement the ten percent of bonnet lairds with the richest fiefs (using much the same metric as for the wealth of markets) become barons and build castles.

Rendering the buildings

This seems to me to provide an algorithmic means of settling a landscape which will generate organic and satisfying patterns of settlement. But it all fails if the buildings are chosen from a limited palette of models. As with the trees I think we need algorithmic mechanisms of building similar-but-different buildings which can be repeatably rendered from relatively small data sets. As an example of what I mean, in damper landscapes where wood is likely to be available, there might be a higher probability of stave buildings, or weatherboarding, with mainly shingle roofs. In slightly less damp areas where timber is still available, cruck frames and half timbered buildings will prevail, with mostly thatched roofs. In the dryest areas, cob and brick buildings will be common, often with tile roofs. On steeper hillsides, stone buildings will be common, perhaps with slate roofs. Within each of these types there are essential cells from which a building is created. These cells can be longer or shorter, taller or lower, wider or narrower. A building may comprise a single cell, or more. If more than three cells they may be arranged in a row or round a courtyard. And they may have one story or two. Which they have can be based – like the details of the plants – on functions which take latitude and longitude as arguments and which, internally use pseudo-randoms seeded from those latitude and longitude values.

How vast a world?

OK, so, with this general approach, how big can we go? The answer seems to me to be 'big enough'. A 32 bit integer gives somewhat over four billion values, so can resolve down to one millimetre precision in a world 4000 kilometres by 4000 kilometres. But we don't actually need millimetre resolution; centimetre would be quite small enough. And that gives us potential for a world 40000Km square, or 1.6 billion square kilometres, which is three times the surface area of planet Earth.

In practice we can't go that big for all sorts of space and time reasons. Recording land heights is inevitably an issue. I don't know of a pseudo random function which will generate satisfying land heights. Anything based on Julia sets, for example, ends up with landforms symmetrical around a central point. Furthermore, the shapes of fractals which can be constructed from simple functions tend to have a noticable and unnatural degree of self-similarity across scales. I'd dearly like to be wrong on this, but I think we need to store at minimum elevation values at ten metre intervals. If we can accept 100mm resolution for elevations, storing 16 bit values gives a range of 6,500 metres - 21,000 feet - from the deepest seabed to the peaks of the highest mountains.

This means that landform information alone requires 20Kbytes per square kilometre - unindexed, but seeing it's a rigid ten metre grid that isn't a problem. Which, in turn, means that you can store landform information for a planet the size of Earth in one terrabyte. But we don't need a planet the size of earth. Scotland is 80,000 square kilometers of land area; allowing for a bit of sea around to the horizon around it, say 100,000 square kilometers. That seems to me more than big enough to be a game space. It amounts to 160Mb of landform data, which is completely manageable.

If we stored plant data for every distinctive plant in Scotland - even at one per ten square metres - that does become an impractically large data set, because quite apart from anything else, the plant locations do have to be indexed. But actually, given that the actual plants that grow are a function of the location at which they grow, no player is going to notice if the pattern of the locations of plants is the same for each square kilometre. So we can manage plant data for a land area the size of Scotland in 400,000 bytes - we could do it in less (if the locations were generated using a pseudo-random function, much less).

Building data is different. We need to store the latitude, longitude and type of every building explicitly, and again they need to be indexed in order that we can recover the buildings in a given area efficiently. We need about 16 bytes per building (four bytes latitude, four longitude, two type; then for each tile a null-terminated vector of pointers to building records). If we assume that our feudal land of 80,000 square kilometers has a population of a million, and that there are on average five occupants of every building, that's two hundred thousand buildings, implying 3.2Mb of data.

Of course, that's just the backing store size. As tiles are loaded into active memory - see the essay 'Tiles and Flats' this raw backing data has to be inflated procedurally into actual models that can be rendered; models which may have thousands of vertices and hundreds of kilobytes of textures. The functions which do that inflating have some finite size, and, significantly, they'll need to work on prototype models which will in turn take storage space. Finally there are hand-edited models potentially used at particular plot locations; those need to be stored more or less in full. But all this has not become an unmanageable amount of data. It seems to me plausible that you could store a fully populated 100,000 square kilometer game world on one uncompressed 700Mb CD. On a 4Gb DVD, you could do it very easily.