Lorenz (and related) Pixmap



Width: Height:
Colours: x from to y from to z from to
Time Step: Steps Per Frame:

x0 = + screen_x (0-1) * + screen_y (0-1, bottom=0) *
y0 = + screen_x * + screen_y (0-1, bottom=0) *
z0 = + screen_x * + screen_y (0-1, bottom=0) *

A take on the Lorenz System - a classic study in chaos theory. Rather than representing the x, y and z variables as positions, this code represents them as RGB components; x as red, y as green, z as blue. You can adjust the ranges of x, y and z that the colour components map on to. Each pixel represents a single Lorentz system, and the position on the chart represents different initial conditions and/or parameters. Tweak the parameters, click Reset, then click Auto-Iterate to get the thing moving. Click Stop to pause, click on the chart to look at the current and initial conditions and the parameters at that point on the chart - and to plot the Lorenz attractor at that point, then click Auto-Iterate to restart. Click and drag with the left or right mouse button (they do different things) to rotate and zoom the view of the Lorenz attractor.

There's also the option to use different sets of differential equations. I've also included the Rössler system, the Rabinovich–Fabrikant Equations and a version of the equations describing Chua's Circuit - taking the exact equations from this simulation.

Peter Corbett, 2014

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