The simplest example of a fractal to visualize is to draw a straight line. Draw two more lines branching from the first in a Y shape at half the length. Do this to the end of every line until you get bored, and you have just barely started making a fractal.
Fractals can be seen in nature in an array of manifestations. The spiral of a snail shell, the recursive diamonds of a sunflower, and the hexagonal crystal patterns of pyrite. All of these share a distinct trait of repeating a recognizable pattern at multiple scales.
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MANDELBROT z7 2D FRACTAL EXTENTS