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

.

References

[1] J. Hawkins, L. Koss, and M. Taylor. "Julia Sets of Weierstrass Elliptic P functions with Toral Band Fatou Components," linked from Graphics Images of Julia Sets of Nonpolynomial Maps. (Nov 11, 2014) www.unc.edu/math/Faculty/jhawkins/graphics.html.

External Links

Fractal (Wolfram MathWorld)

Mandelbrot Set (Wolfram MathWorld)

WeierstrassP (Wolfram Documentation Center)

Weierstrass Elliptic Function (Wolfram MathWorld)

Permanent Citation

Enrique Zeleny

"Fractals Generated by the Weierstrass P Function"
http://demonstrations.wolfram.com/FractalsGeneratedByTheWeierstrassPFunction/
Wolfram Demonstrations Project
Published: November 12, 2014