The science of
possible forms.

Thompson studied living forms through geometry, scale, growth, and physical forces. His transformations of coordinate grids offered a way to compare related shapes by changing the space in which they were drawn. His work makes the construction of form itself a subject of inquiry.

For Protobytes, this suggests a productive question: what rules and constraints could produce a body? Thompson’s account of form and mechanics is distinct from the population selection used in genetic algorithms. Both can inform a practice that studies how bodies arise and how they function.

Primary text: D’Arcy Wentworth Thompson, On Growth and Form, Cambridge University Press, 1917. See chapters XVI–XVII on mechanical efficiency and transformations.

Turing proposed that interacting and diffusing chemical substances could generate spatial patterns from an initially near-uniform state. His model made a connection between local processes and the emergence of organized structure.

This offers a scientific connection for thinking about generative pattern and development. The connection is conceptual here: a patterned protobyte surface should only be described as a reaction–diffusion system when its implementation actually uses that mechanism.

Primary paper: A. M. Turing, The Chemical Basis of Morphogenesis (PDF), Philosophical Transactions of the Royal Society B 237, 37–72, 1952.

Holland developed a foundational account of adaptive search using populations, selection, and genetic operators. In a genetic algorithm, a coded candidate is evaluated, selected candidates contribute to offspring, and variation supplies new possibilities.

In the maze study, the genome encodes body parameters and a neural controller. Mutation and crossover change those values; performance in shared trial environments influences reproduction. “Fitness” means a score under those particular conditions. It carries no universal ranking of creatures.

Primary book: John H. Holland, Adaptation in Natural and Artificial Systems, first published 1975; linked MIT Press edition, 1992.

Sims evolved both virtual body structures and neural systems that controlled their movement in simulated physical worlds. Different evaluations encouraged behaviors including swimming, walking, jumping, and following.

This is a close precedent for the project’s interest in motility: the capacity to move through a creature’s own activity. It also gives us a useful distinction. Evolving a gait for a chosen body is a narrower experiment than evolving body structure and control together. The earlier Protobytes gait studies and current navigation model are described at their actual scope in the notebook.

Primary paper: Karl Sims, Evolving Virtual Creatures (PDF), SIGGRAPH ’94, 15–22. Watch Sims’s original study ↗

Lehman and Stanley showed that rewarding behavioral novelty could overcome misleading objectives in their maze-navigation and biped-walking experiments. This matters when a route to success requires temporarily moving away from an apparent goal.

Primary paper: Joel Lehman and Kenneth O. Stanley, Abandoning Objectives: Evolution Through the Search for Novelty Alone (PDF), Evolutionary Computation 19(2), 189–223, 2011. DOI: 10.1162/EVCO_a_00025.

Mouret and Clune’s MAP-Elites retains high-performing solutions across a space of chosen characteristics. It offers a way to examine many different successful forms and behaviors.

Primary research preprint: Jean-Baptiste Mouret and Jeff Clune, Illuminating search spaces by mapping elites, 2015.

These are possible directions for Protobytes. The current maze implementation uses objective-based selection with an exploration reward; it does not yet implement novelty search or MAP-Elites. Preserving different useful behaviors would be a meaningful next step toward a more varied population.