Delta Diffuse uses reaction-diffusion simulations to create complex patterns

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Delta Diffuse

Delta Diffuse, designed by Nolan Kim, is the design and development of an outsole that Reaction-Diffusion configures. Reaction-diffusion systems simulate the progressive interaction between two reactive chemicals. Nolan also 3d printed Delta Diffuse as a prototype.

Simple adjustments to the initial conditions can produce a wide range of spatial patterns. Each variation serves as a framework for understanding biological pattern formations (e.g., fish scales, reptile skin, coral growth, leopard spots, and zebra stripes). The Gray-Scott Diffusion Model is a mathematical equation that emulates Reaction-Diffusion patterns. The equation is recursive, meaning it uses the previous value to inform the subsequent value. This allows the growth behavior to evolve over time.

3D-printed model

The main variables that influence the type of pattern that emerges are the diffusion rates of chemicals ‘A’ and ‘B,’ the feed/kill rates of each chemical, and a Laplacian function. The Laplacian function drives the diffusion part of the reaction, as it returns the difference between a particular cell and the average of its adjacent cells. This is done by applying a blur or noise function to the starting chemicals.

By adjusting the values of the ‘feed’ (f) and ‘kill’ (k) rates, it’s possible to unlock a wide range of patterns, from circular spots to oscillating stripes. Pearson’s Classification of this relationship is a useful tool that categorizes the expected types of formations when using certain input ‘f’ and ‘k’ values.

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