The Fractal Science Kit fractal generator is a Windows program to generate a mathematical object called a fractal. The term fractal was coined by Benoit Mandelbrot in 1975 in his book Fractals: Form, Chance, and Dimension. In 1979, while studying the Julia set, Mandelbrot discovered what is now called the Mandelbrot set and inspired a generation of mathematicians and computer programmers in the study of fractals and fractal geometry. Kleinian Group (Orbit Trap)Like other mathematical ideas, fractals involve numbers and equations. Unlike most other mathematical ideas, fractals can be used to generate complex, beautiful images that appeal to mathematicians and children alike. Swirling spirals, endless self-similar repetitions receding into the distance, geometric objects arranged in infinitely complex patterns, plant-like creations, geologic designs, clouds, and more, comprise the fractal landscape. These wondrous patterns defy logic yet owe their very existence to mathematics and computers. See the Fractal Image Gallery for some examples of the myriad of fractal designs possible. Mandelbrot FractalA fractal image is created by evaluating a complex equation or by performing a sequence of instructions, and feeding the results back into the equation over and over again. During the iteration, you accumulate statistics and map the resulting data to colors, creating the fractal image. By varying the equation or the instructions, you can create Mandelbrot Fractals, Orbital Fractals, L-System Fractals, Orbit Traps, and more. Mandelbrot FractalThe Fractal Science Kit fractal generator provides a rich framework for exploring the world of fractals. It handles the common processing steps required to generate a fractal image so that you can concentrate on the fun part; developing the fractal formulas/equations, complex transformations, and coloring schemes that define the fractal. Symmetric Icon (Orbital Fractal)This is not to say that you must write code to use the Fractal Science Kit. On the contrary, hundreds of Built-in Programs are available right out of the box and most of these provide options that yield countless variations. A fractal image is the result of combining an equation with data collection programs, complex transformations, and color controllers (the instructions that map the data to colors). By choosing different combinations of these programs/options, you can generate more fractal images than you could ever hope to view in your lifetime without ever writing a single line of code. Julia Fractal (Phoenix)The Fractal Science Kit fractal generator supports many different Fractal Types including: Mandelbrot, Julia, Convergent, Newton, Orbit Traps, Sierpinski Triangle, IFS, Strange Attractors, Rep-N Tiles, Symmetric Icons, Symmetric Attractors, Frieze Group Attractors, Wallpaper Group Attractors, Hyperbolic Attractors, Apollonian Gasket, Circle Inversion, Schottky Group, Kleinian Group, L-System and many more. Hundreds of built-in equations, transformations, orbit traps, and color controllers, allow the casual user to produce stunning fractal images while providing the experienced fractal developer a rich set of illustrative examples on which to build his/her own fractal programs. Kleinian Group (Orbit Trap)The Fractal Science Kit fractal generator provides an interactive programming environment with Application Windows for viewing the fractal image, modifying the properties that define the fractal, examining the data behind the fractal, and viewing/editing the fractal programs, macros (inline functions/methods), and color gradients, used by the Fractal Science Kit to produce the final image.
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