Fractals Generated by the Weierstrass P Function

a

0.708

b

0.854

c

0

1.

x

0.1

y

0.1

r

10.

d

0.18

δ

0.002

The definition of the Mandelbrot set is based on the mapping

z↦

2

z

+c

. This Demonstration uses a variation of the mapping,

z↦c(℘(z;a,bi)+

c

0

)

, where

℘

is the Weierstrass function,

a

,

b

, and

c

0

are real, and

c

is complex. The escape radius is

r

, the initial value is

x+iy

(restricted to be in a

2d×2d

region), and the function is computed at resolution

δ

.