I have a developed an unending fascination with The Mandelbrot Set.

One of the set’s most well-known features is the cardioid which makes up the inner bulb shape. This really cool video explains how to create a cardioid using a circle and a simple multiplication table.

The formula to construct the traditional Set is Z = (Z*Z) + C. Inspired by the video, I updated my OOJS Mandelbrot Set project to use a slightly different formula:

Z = (Z*Z*Z) + C

The resulting image now features a nephroid as the primary feature, instead of a cardioid. Nephroid means kidney-shaped.

In the first case, our exponent was 2 and we saw 1 bulb. In this case, our exponent is 3 and we see two bulbs. This pattern continues: as the exponent (n) value increases, the number of bulbs is n - 1. These shapes are known as Epicycloids.

images generated with https://github.com/lombardo-chcg/OOJS-Mandelbrot-Set

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Z = (Z**3) + C

nephroid mandelbrot set

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Z = (Z**4) + C

three bulb mandelbrot

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Z = (Z**10) + C

nine bulb mandelbrot