Devlog (3): AlgoRhythms

Hi,

Let's take a look at the broader scientific and computational theories that I'm exploring in my work within Xylem. 

Computational Models and Theoretical Foundations

• Cellular Automata (CA): A model where cells on a grid evolve through discrete time steps according to a set of rules based on the states of neighboring cells. It's one of my favorite conceptual tools. 
• Graph Theory: A branch of mathematics focusing on graphs (🙃), which are structures made up of nodes connected by edges. This junk is crucial for modeling relationships, and has shown up in every project I've every worked on in some way.
• Algorithmic Information Theory (AIT): A domain studying the amount of information required to represent objects, and the computational resources needed to generate them.  There's potential for themes and narrative development here.
• Wave Function Collapse (WFC): A procedural generation algorithm that uses simple rules to output complex, interconnected patterns. I want to abuse this in some way - possibly in a more discrete under-the-hood sort of way.

Evolutionary and Genetic Models

• Genetic Algorithms (GA): Optimization algorithms.  These mimic biological evolution, where solutions evolve to optimize a given fitness function.
• Morphogenetic Algorithms: These algorithms draw from the biological process of morphogenesis, focusing on how the shape and form of organisms develop and shift.  I’m interested in using this both for the organisms but also in working with biomes and biome-to-biome interaction.

Neural and Cognitive Models

• Artificial Neural Networks (ANN): Computing systems inspired by the neural networks of brains, capable of learning and/or making decisions by pushing inputs through layers of interconnected nodes.
• Spiking Neural Networks (SNN): Similar to an ANN, a type of neural network that mimics the way biological neurons spike and communicate.  I think a "turn-based-time-constant' kind of vibe fits here.
• Neural Field Models: Mathematical models that describe how neural signals spread across areas of the brain or nervous system. I suppose it could be described as a birds-eye-view of the collective neural dynamics.

Swarm and Multi-Agent Systems

• Multi-Agent Systems (MAS): Systems in which multiple autonomous agents work together to achieve certain goals, modeling complex behaviors in so-called 'distributed environments'.
• Swarm Intelligence: The collective behavior of decentralized, self-organized systems, such as colonies of ants or flocks of birds, used to solve problems or optimize tasks.  Between this and MAS, I feel like there's an interesting space for organisms to communicate and have a greater emergent complexity.
• Slime Mold Algorithms: Optimization techniques inspired by the networks formed by slime molds.  These can affect decentralized problem-solving strategies.  Plus slime molds are cool.

Complex Systems and Dynamics

• Hypernetworks: Extensions of graph theory allowing for modeling of higher-order interactions. I can see using this with fluid or power simulation for machine tiles.
• Reaction-Diffusion Systems: Mathematical models that describe how the concentration of substances in some space change under both local reactions and diffusion.
• Nonlinear Dynamical Systems: Systems in which small changes can lead to disproportionately large effects. Plus fractals are cool...

Stochastic Models

• Markov Chains: A stochastic model utilizing probabilities to predict future events based  upon the current state of a system.  Now let me make the stochastic parrot.
• Lévy Processes: Broad class of stochastic processes with independent increments.  Likely I'll lean into Lévy Flights for plant classes of organisms.

Each of these offers a potentially strange lens through which the complexities of life sim behaviors can be explored.  There's a lot I want to do with Xylem, and hopefully these will provide a kind of stratum to plant my mind in while I work.  Let me know if anything here catches your eye, or you've got your own pet algorithm or field I should know about!

Eli