Luz: Clifford Attractors Plugin

Introduction

Today I’ve been diving into the works of Clifford A. Pickover after reading some of his early books on computer graphics when I stumbled over the Clifford Attractor on Paul Bourke’s homepage.

These chaotic attractors can produce stunning visualizations and with example code provided by Paul Richards, I was able to write a plugin for Luz that could render them in real-time. Paul Bourke goes into more detail further down in the page about how these color effects are achieved:

The main thing happening here is that I don’t draw the attractor to the final image. Rather I create a large grid of 32 bit (int or float) and instead of drawing into that in colour I evaluate points on the attractor and just increment each cell of the grid if the attractor passes through it.

So it’s essentially a 2D histogram for occupancy. One wants to evaluate the attractor much more/longer than normal in order to create a reasonable dynamic range and ultimately smooth colour gradients. I then save this 2D grid, the process of applying smooth colour gradients comes as a secondary process … better than trying to encode the right colour during the generation process. One can even just save the grid as a 16 or 32 bit raw, open in PhotoShop and apply custom gradient maps there.

Of course this is “just” a density mapping of the histogram and doesn’t immediately allow for colouring based upon other attributes of the attractor path, such as curvature. But such attributes can be encoded into the histogram encoding, for example the amount added to a cell being a function of curvature.

Plugin Demo

Alongside playing around with the Clifford Attractor, I’ve added a couple of minor features to Luz:

• A grid for the viewport to replace the grey default background
• Replaced performance overlay with a dedicated performance graph to record render times
• The option to save the currently rendered image from the viewport to disk
• Frame buffer label overlay on the rendered image

Gallery

Here is a presentation of the Clifford Attractors I rendered during my session, they are somewhat grainy but the result is nevertheless pleasing to look at.

Until next time, have a good weekend!