Friday, 10 August 2007

Cartography



Intrepid Electron continues her string of inventions. Yesterday she invited me to the Crash Me Sim (which I found to be quite a novelty) to show off a script that generated a three-dimensional cartographic representation of the sim it surveys, using nearly 10,000 prims. It goes without saying the sim is otherwise empty. She then showed me a fractally generated tree. I don't know if she is the first to try this in SL (I have seen no other, though I should be surprised if no one else has tried to create them), but it seemed a fairly straight forward application of Lindenmayer systems (I may have been born in the Eighteenth Century, but I do keep up with my reading). No relation to Linden Lab as far as I know, Lindenmayer systems were conceived in 1968 as a mathematical theory (really just a formal language) of plant development by Hungarian biologist Aristid Lindenmayer (1925-1989). Lindenmayer systems define complex objects by successively replacing parts of a simple initial object using a set of rewriting rules. A beautiful book in my library describing the theory and its many applications titled The Algorithmic Beauty of Plants is well worth perusing, and I discovered the 1990 print edition is available online in its entirety (scroll to bottom of linked page for the pdf) !

I have always understood the taxis, genera, parataxis and entaxis of classical architecture (no, I refer not to cabriolets for hire) form an L-system, and by replacing the entire space a building occupies with it major parts (building -> roof, walls, floor), and each of those parts by its component parts (wall -> column, window, column, door, column, window, column) , and so on (column -> entablature, capital, shaft, base) down to the elements themselves (ionic capital -> abacus, volutes, echinus), one can describe an entire grammar of classical architecture. Alexander Tzonis and Liane Lefaivre at the Technische Hogeschool, Delft, explored this underlaying grammar in their Classical Architecture: the Poetic of Order (1986). I am not confident the same could be said for modern or contemporary architecture, which appears to me generated by different rules.

Further one might automatically generate a variety of buildings (as easily as Electron generated her tree) by encoding the grammar into lists, replacing list elements with other lists in a recursive fashion, and applying simple rules to resolve the resulting list as a set of prims.

Returning to trees, my only wish would be that it look more like a natural tree! This of course means matching carefully the angles of the generated components to what one observes in nature, and perhaps replacing some generated terminals (smaller branches, or clusters of leaves) with alpha matted images on flat prims.

But it was an inspiring presentation!

2 comments:

Enjah Mysterio said...

What a terrifying post ... your mathematical confidence inspires awe.

Young Geoffrion said...

More bravura than confidence, Enjah! And what I understand is language, not mathematicks. What terrifies is only my scattered and dissipate interests, and my willingness to pretend toward knowledge.