PROGRAMMING PARADIGMS

Do You Have a Future in Vegetative Virtuality?

MICHAEL SWAINE

My garden will never make me famous, I'm a horticultural ignoramus, I can't tell a string bean from a soybean, Or even a girl bean from a boy bean.

--Ogden Nash

I think that I see an undiscovered product niche. It's a vertical product niche, with thousands of potential customers and the prospect of multiple sales to each customer. The niche is virtual shrubs.

Macintosh-Aided Design magazine recently ran a good article on landscape design, 3-D graphics, and vegetable verisimilitude. Daniel Earle's "Three-Dimensional Representation of Plants in Landscape Design" (June, 1990) described how landscape designers and architects can use 3-D modeling tools to produce the perspective views of trees and shrubs necessary in their work.

Current 2-D object-based approaches, according to Earle, allow creating libraries of plant symbols, and freehand drawing programs produce acceptable freehand results; but 3-D modeling approaches have not been impressive: Present computer approaches that create plants that look like lollipops, rockets, or shaped concrete do not adequately satisfy planting design considerations. It's necessary that plant forms exhibit freedom, variety, and organic form, otherwise they look like extensions to the hardscape around them, rather than offering a contrast.

Earle proposes using 3-D graphic tools to model trees and shrubs, rather than just patching together a few geometric forms. He identifies essential elements of structure and form of plants, and shows how to develop, without excessive effort, workable plant forms.

It struck me as I read the article that it ought to be possible to do better than workable plant forms and that it ought to be easier. Earle's approach definitely leads to better-looking trees and shrubs, but it's ultimately not different in kind, but only in degree, from the 2-D plane geometry models he criticizes. Trees aren't really made up of plane geometry objects and conic sections. Why not use fractals?

As I've pointed out here before, fractal geometry, the new branch of mathematics that Lucas films has used to produce pseudonatural forms in science fiction movies, is remarkably good at modeling natural forms such as coastlines, mountain ranges, and foliage. Certain classes of fractals are particularly good at mimicking trees and shrubs. This is because, so far as I can understand it, the recursive growth pattern of the fractal reflects a similar growth pattern in nature. Fractals know some of Nature's algorithms.

My own explorations through the maze of these shrubby fractals have run up against two thorny hedges: performance and predictability. Fractal algorithms are viciously recursive, and any more than a few levels of recursion takes unacceptably long to execute on my hardware (and more to the point, in my code, but improving the code will only shift the performance barrier back a few levels). Further, although I have generated some attractive and natural-looking plant forms, the process is hit-or-miss: I don't know the relationship between the parameters I can manipulate and the defining features of the sorts of plants I can model.

For the needs of landscape designers, it seems to me, the performance problem is not critical. Their needs are for simple but evocative and recognizable images. A picture should be recognizably a birch tree or a particular variety of succulent, but rich detail is not desirable. Even the simple algorithms and implementations I've played around with should be able to meet these performance requirements.

If the predictability problems were solved, fractals would, I think, take over the field. The advantages are compelling:

Greater naturalness. The controlled randomness of fractal techniques gives a more natural image than does building from conventional geometric forms.

Deep naturalness. Fractal geometry apparently accurately models the process of growth and the underlying grammar of the natural forms it simulates.

Greater efficiency. Fractal images have absurdly modest storage requirements, if stored in the form of the generator function and generated at need.

Greater power. Fractal techniques use recursive image generation to allow any level of detail to be produced from a single stored generator function.

Now, apparently, the predictability problem has been solved. Michael Barnsley, co-founder of Iterated Systems, Norcross, Georgia, has found that by starting with a digitized natural image, say, of a coastline, and mapping segments of it to a large library of standard fractal-like transformations, you can turn the image into a formula that does a credible job of reproducing the image, at an acceptable video rate, with a compression ratio of perhaps 500:1! Barnsley has turned the insight into a business, but he doesn't seem to be filling the niche I think I see, and the basic insight is not proprietary.

So I think that somebody is going to make money selling libraries of virtual shrubbery. Libraries of natural-looking trees and shrubs ought to speed the landscape designer's work, and ought to sell well.

The simplest implementation of the idea would be to set up a plant plant (wait, make that a virtual shrubbery nursery), and to crank out libraries of plant forms in a standard 3-D format. This approach, though, would lose some of the benefits of using fractals. The desired amount of detail could vary, and a fractal generator function can lay on as much detail as you can sit still for. Perhaps a better distribution model would be as a smart picture; some sort of object, containing the generator function, an interface allowing the input of a recursion level, and the minimal code required to execute the generator function, to unfold the function into a graphic image. The recursion level would control the degree of detail in the resulting image.

By creating such smart plants, one would belie the old saying, "You can speed up horticulture but you cannot make it think."