Fractals
From GenerativeArt
(Difference between revisions)
* Some mathematical functions define sets of points where the boundry between in-set and out-of-set points exhibit self-similarity across scales. e.g. The Julia set, the Mandelbrot set, and others. | * Some mathematical functions define sets of points where the boundry between in-set and out-of-set points exhibit self-similarity across scales. e.g. The Julia set, the Mandelbrot set, and others. | ||
* In chaotic systems a phase diagram will exhibit fractal behavior about a strange attractor. (To be covered later). | * In chaotic systems a phase diagram will exhibit fractal behavior about a strange attractor. (To be covered later). | ||
| + | |||
| + | Fractals can be defined and generated by recursive functions. | ||
| + | Example: Factorial Function | ||
| + | '''Non-recursive''' | ||
| + | '''function''' FACT(m) | ||
| + | total = 1 | ||
| + | '''for''' n = 1 to m | ||
| + | total = total * m | ||
| + | '''end''' | ||
| + | '''return''' total | ||
| + | |||
| + | '''Recursive''' | ||
| + | '''function''' FACT(m) | ||
| + | '''if''' m > 1 | ||
| + | '''return''' m = m * FACT(m-1) | ||
| + | '''else''' | ||
| + | '''return''' 1 | ||
| + | '''end''' | ||
