Stark Raving Math

The images in these pages were generated mathematically, on a small computer, using a combination of fractal geometry, raytrace rendering, and desktop publishing software. They can be thought of as extremely large mosaics. Each "tile" is a number, and each of these numbers represents a specific color. In computerese, these tiles are known as picture elements or "pixels", and appear as the individual dots (on the computer's display or the printed page).

Fractals

Fractal geometry is one of Stark Raving Math's specialties. The study of numerical functions with a fractional dimension is a powerful mathematical tool, which has been used by researchers and designers alike, to emulate many natural processes and other similarly self-connected systems. Careful inspection shows that patterns in fractal objects systematically repeat themselves withstring limit. The apparently random shape of a cloud, the interlocking growth pattern of most plants, the branching flow of a river and its tributaries; all of these are examples of Mother Nature's preference for forms that interact with each other and repeat themselves.

To model this behavior, iterative formulas are constructed where relatively simple arithmetic calculations are repeated over and over, feeding the results of each step back into the next. That way, each pixel is computed partly based on the values of its neighbors. These formulas are, quite literally, infinitely complex. The speed and capacity of the computer on which they run is the only limiting factor. Fractals reveal more and more detail, as you plot smaller and smaller areas. Colors are assigned to numbers in the equations, and the computer prepares visual images by plotting them on a grid.

RayTracing

Stark Raving Math also uses a technique called "raytraced rendering", one of many approaches to three dimensional computer modeling. This method can create fantastic, surrealistic images with an almost photographic look. The raytracer is a program which reads a list describing the shapes and textures of objects, the color and location of light sources, and the position of an imaginary camera. Using this information, it mathematically simulates the rays of light moving through the scene; allowing it to properly mimic shadows and light, perspective, reflections and refractions.

For every pixel in the final picture, the raytracer "fires" at least one "ray" through that pixel into the simulated world, to see what it hits. For each hit, it calculates rays to each of the lights to see if that spot is being illuminated. That all adds up to lots of rays! And every ray must be tested against every object. For that reason, ray tracing is not a fast process. But, the results are worth the wait: synthetic images with entirely believable camera angles, shadows, reflections, and other effects.

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