HOME | DD

Description
A still frame from an animation of a sequence of random walks that create fractal octagons. In this example the octagons overlap slightly at every scale. The larger green dot marks the start of the random walk. Grey dots mark the steps in the walk - there are 1 million. The large red dots mark the positions of the attracting points. At each step the walk goes a fraction of the distance from its current position towards one of these red dots. Which one is selected randomly with equal probability of each. The fraction used is constant throughout the walk. The value of this fraction determines the extent of overlap of the octagons. A smaller fraction leads to less overlap and eventually increasing separation of the octagons.

Description
A still frame from an animation of a sequence of random walks that create fractal octagons. In this example the octagons overlap slightly at every scale. The larger green dot marks the start of the random walk. Grey dots mark the steps in the walk - there are 1 million. The large red dots mark the positions of the attracting points. At each step the walk goes a fraction of the distance from its current position towards one of these red dots. Which one is selected randomly with equal probability of each. The fraction used is constant throughout the walk. The value of this fraction determines the extent of overlap of the octagons. A smaller fraction leads to less overlap and eventually increasing separation of the octagons.