Strange attractors are a specific type of dynamical system that creates an attractor with a fractal structure. In this research I explored applications of strange attractors in generative design applications by developing mapping algorithms to apply the features of strange attractors to 3D geometry.
Process
Attractor systems were programmed in Houdini and once initial conditions were seeded, geometry was generated using a solver. Generated point values are normalized - all values for single-point initialization and the most recently generated values for each point with multi-point initialization. An output seed and output mapping variables applies those values to desired geometry.
Output Mappings
Some examples of output mappings are a basic heightmap conversion from a multi-point initialization setup, and dynamic radius control with variance controlled by the resolution of the attractor solver. In the example below, both sets of baskets were generated with the same attractor seed and values but different solver resolutions, demonstrating variance control with this mapping system.
Animating Outputs
Caching the generated solver values can allow for animated output mappings.
This method is more computationally expensive than more traditional simplex or perlin noise algorithms, but yeilds visually unique results. It benefits from fairly predictable re[ppetitive patterns, while leveraging the fractal nature of strange attractors to generate completely unique output values for every seed value.
This research was presented at CUR's National Conference on Undergraduate Research and as a plenery presentation at Harvard's National Collegiate Research Conference in 2021.