Controlling Chaos: a Simple Deterministic System for Creating Complex Organic Shapes

It is difficult and frustrating to create complex organic shapes using the current set of computer graphic programs. One reason is because the geometry of nature is different from that of our tools. Its self-similarity and fine detail are derived from growth processes that are very different from the working process imposed by drawing programs. This mismatch makesit difficult to create natural looking artifacts. Drawing programs provide a palette of shapes that may be manipulated in a variety ways, but the palette is limited and based on a cold Euclidean geometry. Clouds, rivers, and rocks are not lines or circles. Paint programs provide interesting filters and effects, but require great skill and effort. Always, the details must be arduously managed by the artist. This limits the artist's expressive power. Fractals have stunning visual richness, but the artist's techniques are limited to those of choosing colours and searching the fractal space. Genetic algorithms provide a powerful means for exploring a space of variations, but the artist's skill is limited by the very difficult ability to arrive at the correct fitness function. It is hard to get the picture you wanted. Ideally, the artist should have macroscopic control over the creation while leaving the computer to manage the microscopic details. For the result to feel organic, the details should be rich, consistent and varied, cohesive but not repetitious. For the results to be reproducible, the system should be deterministic. For it to be expressive there should be a cause-effect relationship between the actions in the program and change in the resulting picture. Finally, it would be interesting if the way we drew was more closely related to the way things grew. We present a simple drawing program which provides this mixture of macroscopic control with free microscopic detail. Through use of an accretion growth model, the artist controls large scale structure while varied details emerge naturally from senstive dependence in the system. Its algorithms are simple and deterministic, so its results are predictable and reproducible. The overall resulting structure can be anticipated, but it can also surprise. Despite its simplicity, it has been used to generate a surprisingly rich assortment of complex organic looking pictures.