Technique · Simulations
Attractor cloud
Clifford and de Jong attractors: orbits that never repeat, built up as a glowing cloud whose threads flow as the formula wanders.
Attractor cloud is a simulation that evolves step by step. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- The orbit of a Clifford attractor stays inside a box: since sine and cosine never exceed one, x never goes beyond 1 plus the size of c, and y beyond 1 plus the size of d.
- The glow is an estimate of how much time the orbit spends in each place, which mathematicians call its natural measure; the thin bright threads are places the orbit visits again and again.
- Fractal flames, which Scott Draves developed in the 1990s, extend the same idea, a point moved over and over and lit where it lands, with many formulas chosen at random and with colour added along the way.
- Clifford Pickover, a researcher at IBM, popularised the family of formulas that bears his given name; Paul Bourke's web pages in the 1990s did the same for it and for the de Jong formula, with galleries of settings worth trying.
- Each setting of the four numbers gives a different shape, and most give nothing worth seeing: the pictures here come from a few settings found by searching, which is how every collection of attractors is made.
The mathematics
- The Clifford map is x' = sin(-1.400 y) + 1.000 cos(-1.400 x), y' = sin(1.600 x) + 0.700 cos(1.600 y), so x stays within 2.00 and y within 1.70.
- Two orbits that start close together soon end up far apart, but both draw the same picture; chaos means the path is unpredictable, not that the shape is.
- A frame moves 84,000 points one step each, and the light of earlier frames fades by 8 percent a frame, so about a dozen frames of orbit are on screen at any moment.
In art
- Attractor pictures were among the first to show that chaos could be beautiful; they became posters, screensavers and a staple of early computer art in the 1980s and 1990s.
- Colouring by direction of travel turns a single orbit into a weave of ribbons, because orbits cross the same place heading in different directions at different times.
More ways to use it
Related techniques
Reaction-diffusion · Cellular automata · Sandpile · Grain growth · Slime mould · Flocking boids · Elementary automaton · Synchrony