Fractals

From Big Concept Wiki
Jump to navigation Jump to search

A fractal is a structure consisting of patterns that exist independent of scale.

exponential curve
Mandelbrot set
Von Koch curve

Examples:

  • Photos of the moon zoomed in by different amounts will look similar because lunar craters of all sizes exist.
  • No matter how much you zoom out of a simple exponential curve, the overall shape of the curve will not change because its shape is independent of scale.
  • Geometric fractals, like the The Mandelbrot Set and the Von Koch curve (see images)
  • Network fractals: centralized networks can exhibit fractal patterns with respect to the connectivity of nodes. Some nodes are more connected, some are more connected, and some are even more connected than that, ad infinitum.
  • Similarly, tree patterns (for example, binary trees) can exhibit fractal patterns. In a binary tree, each node has one parent and two children, regardless of it's place on the tree (the only exception being root or head nodes, which can have fewer parents or children). Other tree structures can also exhibit fractal patterns. For example, imagine an army wherein each leader was commanded by 1 man, and commanded 10 men.