This video was made with Mathematica 7. The six changing shapes in the video are called attractors. They are graphical forms of a simple mathematical formula attributed to Peter de Jong. At any given moment the way a single attractor looks depends only on four numbers. A slight variation in these numbers can remarkably change the appearance of an attractor. This is why there are so many different shapes and, while the numbers change continuously during the video, the shapes are so fluid, fleeting and flickering. Every frame of the video consists of 600,000 black points on a white background. There are 4,000 frames and therefore the whole video is a dance of 2.4 billion points conducted by a mathematical formula.
Peter de Jong formula:
x’=sin(a y)-cos(b x)
y’=sin(c x)-cos(d y)
The code of the video is based on an example from The Wolfram Demonstration Project:
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