Most physics simulations are based on the idea that if the state of a system at a particular moment can be represented as data, the next state can be calculated from that data. The next state is computed based on the data, which updates the data, and the process repeats. These types of systems are called feedback systems, as they form a loop where the system's output feeds back into its input.


We briefly mentioned feedback on the image processing page. Here, we will take a closer look at it from a simulation perspective. In the Image Processing page, it was stated as follows:


In the context of image processing, feedback refers to the recursive application of an effect to its output. The following demo uses the basically same effect as the sine function example above, with a slight modification to reduce the amount of translation per step. The only big difference is that instead of using the original image as input, it captures the result of the effect and uses the deformed image as input for the next frame.


What's interesting is that in computers, images are just data - usually just a big array of numbers that represent the distribution of (color) values in a space. There isn't a clear boundary between processing images and simulating some chemical or physical phenomena. It essentially depends on your interpretation of what these numbers represent.


By considering an image not as an image itself, but for example as a distribution of chemicals in a solution, you can create a feedback system that simulate changes in the state of that space.


Reaction-diffusion model


Reaction-diffusion models are mathematical models used to describe the behavior and interplay of reactions and diffusion in various systems, such as in chemical and biological processes. They combine the effects of chemical reactions and diffusion to see how patterns change over time and space. Because these models can create complex patterns that are beyond imagination from simple rules, it is often used in the context of computer graphics and generative art as well.

反応拡散(Reaction-diffusion)モデルは、化学や生物学的なプロセスなど様々なシステムの振る舞いや、反応と拡散の相互作用を記述するために使われる数学モデルです。 化学反応と拡散の効果を組み合わせて、パターンが時間と空間にわたってどのように変化するかを調べます。簡単なルールから思ってもみないような複雑なパターンを形成することができるので、コンピュータグラフィックスやジェネラティブアートの文脈でもよく用いられます。