Technique · Simulations
Fractal flame
A chaos-game flame: points moved by swirling, spherical and horseshoe-shaped transforms light a feathery shape that unfolds as the transforms turn.
Fractal flame 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 program Apophysis, a free flame editor released in 2001, started a community of flame artists who share their parameters as small text files, often called genomes.
- Each flame is a genome of a few dozen numbers: change one coefficient and the whole picture changes, which is how Electric Sheep breeds new flames by mixing and mutating the genomes of those that people liked.
- Flames are rendered in many millions of steps; a logarithmic brightness curve is essential, because the brightest places are hit thousands of times more often than the faintest threads.
- Scott Draves devised the fractal flame algorithm in 1992 and described it in a paper in 2003; his screensaver Electric Sheep, begun in 1999, lets thousands of computers render flames and its users vote on which should breed.
- The chaos game was used by Michael Barnsley in the 1980s to draw the fern and other pictures from a few transforms; flames add nonlinear variations and colour to the same idea.
The mathematics
- Each step picks one of 3 transforms at random, applies (x, y) to (a x + b y + e, c x + d y + f), and then replaces the result by a weighted sum of variations; because the transforms shrink distances on average, the points settle onto a fixed shape however they started.
- A frame moves 700 points about 157 steps each, and the light of earlier frames fades by 7 percent a frame; the brightness shown is 1 minus e to the power minus the count, raised to a power below one, so faint places are lifted.
- The variations have names and formulas: sinusoidal is (sin x, sin y); spherical divides the point by its squared distance from the origin; swirl turns it by an angle proportional to its squared distance; horseshoe, polar and julia fold the plane in other ways.
In art
- Flames have been printed as large posters and shown in galleries; their glowing, smoke-like look is closer to a photograph of a nebula or a firework than to the hard lines of most fractals.
- Because every flame is a handful of numbers, whole collections can be traded and remixed like musical scores, which is what the Apophysis and Electric Sheep communities do.
More ways to use it
Related techniques
Reaction-diffusion · Cellular automata · Sandpile · Grain growth · Slime mould · Flocking boids · Attractor cloud · Elementary automaton