Over a million developers have joined DZone.
{{announcement.body}}
{{announcement.title}}

Fractal-Like Phase Plots

DZone's Guide to

Fractal-Like Phase Plots

· Web Dev Zone
Free Resource

Learn how to build modern digital experience apps with Crafter CMS. Download this eBook now. Brought to you in partnership with Crafter Software

Define f(z) = iz*exp(-z/sin(iz)) + 1 and g(z) = f(f(z)) + 2 for a complex argument z. Here’s what the phase plots of g look like.

The first image lets the real and imaginary parts of z range from -10 to 10.

This close-up plots real parts between -1 and 0, and imaginary part between -3 and -2.

The plots were produced with this Python code:

from mpmath import cplot, sin, exp

def f(z): return 1j*z*exp(-z/sin(1j*z)) + 1

def g(z): return f(f(z)) + 2

cplot(g, [-1,0], [-3,-2], points=100000)

The function g came from Visual Complex Functions.

Crafter is a modern CMS platform for building modern websites and content-rich digital experiences. Download this eBook now. Brought to you in partnership with Crafter Software.

Topics:

Published at DZone with permission of John Cook, DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

{{ parent.title || parent.header.title}}

{{ parent.tldr }}

{{ parent.urlSource.name }}