A fractal is basically a structure that builds off of itself in smaller, repeating patterns. One real world example is trees…. start with a trunk, then it expands into branches. Which expand into smaller branches. Which expand into smaller branches. Circulatory systems are the same way; starting with large main arteries and branching out smaller and smaller segments. Lightning, snowflakes, river systems, etc can all be described in terms of fractals.
Mandelbrot fractals are clever math formulas that have similar repeating structures.
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