# Fractals Generated by Jacobi Theta Functions

Fractals Generated by Jacobi Theta Functions

The definition of the Mandelbrot set is based on the mapping =+c. This Demonstration uses a generalization of the mapping, =(,q)+c, where is a Jacobi theta function, , and , (over the unit disk) and are complex. The escape radius is , the initial value is , and the function is computed at resolution .

z

n+1

2

z

n

z

n+1

ϑ

m

z

n

ϑ

m

m=1,2,3,4

z

q

c

r

x+iy

δ