Swarm of Levy Fliers
This animation combines Levy flight and swarming. A Levy flier moves in a random direction and by a random length. The step length is drawn from a Levy distribution. This has fat tails compared to a Normal (Gaussian), meaning that large step lengths are quite likely. Wandering Albatross, bumble bees, deer and other foraging animals are suspected of 'using' fat tailed distributions, although there is dispute if it is actually a Levy.
Fat tailed distributions provide a better search strategy because the chance of revisiting a location is lower.
The effect of the fat tails can be seen by adjusting the Levy alpha parameter using the UP and DOWN keys (adjust alpha up to a max of 2, when the distribution becomes Normal, or reduce in steps towards 0.5 - at alpha = 1.0 the distribution is Cauchy). The overall scale can be adjusted with the LEFT RIGHT arrow keys.
Each particle in this swarm has a single neighbour. The overall network is a ring. New particle positions are generated by centring the distribution at the centroid of the current position and the position of the neighbour. Swarming can be switched on and off by pressing 's'. When swarming is off, the distribution is centred on the current position, with no neighbours involved.
The particle network is displayed by default and can be toggled by pressing 'p'.
For visual affect, press 'f' to fill particle and 'R', 'G', 'B' to increment colours. Increase/decrease animation speed with ']' and '[' keys. Press 't' for time lapse drawing, 'r' to randomise and 'i' to return to original settings.
Pause/resume - click on applet for focus, then press spacebar.
Press 'r' to randomise settings; 'i' for initial values.