Fractal Star Function

Science
1

If one modifies the Mandelbrot set, a function for drawing a fractal star of any number of points can be obtained.

Start with the Mandelbrot set:

z[n+1] = z[n]^2 + c

And simply change it to:

z[n+1] = z[n]^(s+1) + c

Where s is the number of points on the star. We can then see that the Mandelbrot set is an approximation to a 1-pointed star if such a thing were to exist. Following are the first 6 stars using this function:

s = 1

s = 2

s = 3

s = 4

s = 5

s = 6

2

Speak of the devil. I was just looking at fractuals the other day. I found it interesting that fractuals parallel my own work in generating real information of the future or the past on a super computer. But I don,t use fractual equations but they can crop up in my work.