Experimental simulation of emergent complexity through graph-rewriting automata.
Rabrg/artificial-life
A simple (300 lines of code) reproduction of Computational Life: How Well-formed, Self-replicating Programs Emerge from Simple Interaction
A Gentle Introduction To Graph Theory
So many things in the world would have never come into existence if there hadn’t been a problem that needed solving. This truth applies to…
Software in the natural world: A computational approach to hierarchical emergence
Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent macroscopic levels; however, while these approaches are successful in identifying when emergence takes place, they are limited in the extent they can determine how it does. Here we address this limitation by developing a computational approach to emergence, which characterises macroscopic processes in terms of their computational capabilities. Concretely, we articulate a view on emergence based on how software works, which is rooted on a mathematical formalism that articulates how macroscopic processes can express self-contained informational, interventional, and computational properties. This framework establishes a hierarchy of nested self-contained processes that determines what computations take place at what level, which in turn delineates the functional architecture of a complex system. This approach is illustrated on paradigmatic models from the statistical physics and computational neuroscience literature, which are shown to exhibit macroscopic processes that are akin to software in human-engineered systems. Overall, this framework enables a deeper understanding of the multi-level structure of complex systems, revealing specific ways in which they can be efficiently simulated, predicted, and controlled.
Co-creating with emergent processes ✦ Hijinx World
Existential musings over algorithmic design with creative programming legend Dan Tapper.
The Facebook Method of Dealing With Complexity
Computers used to be weak, so we had to make their world simple. Now they can handle endless complexity, but we need to learn how to make the world simple
Automata Theory by Javier Esparza
A comprehensive introduction to automata theory that uses the novel approach of viewing automata as data structures.
Structured planning and debugging | Proceedings of the 5th international joint conference on Artificial intelligence - Volume 2
We introduce a new approach to planning in STRIPS-like domains based on constructing and analyzing a compact structure we call a Planning Graph. We describe a new planner, Graphplan, that uses this paradigm. Graphplan always returns a shortest-possible ...
Complexity Explorables
A collection of interactive explorable explanations of complex systems in biology, physics, mathematics, social sciences, epidemiology, ecology and other fields....
Circuit Tracing: Revealing Computational Graphs in Language Models
We describe an approach to tracing the “step-by-step” computation involved when a model responds to a single prompt.
All you need is data and functions
It's really easy to tend towards complexity as engineers. I think on some level, we love complexity. There are obviously bad types of complexity, but I think there are other types of it that we seek out, because there's something satisfying about wrapping your head around it; and I think a lot of that kind of complexity ends up in our programming languages.
Emergence: the remarkable simplicity of complexity
From the fractal patterns of snowflakes to cellular lifeforms, our universe is full of complex phenomena – but how does this complexity arise? “Emergence” describes the ability of individual components…
Mahax on Twitter / X
Head of Claude Code, Boris Cherny:"You're not supposed to write code anymore. You're supposed to build a graph that writes itself."In 30 minutes he breaks down how engineers at Anthropic build graphs that write the code, catch the bugs, and ships.Most engineers build… https://t.co/I3b2Rt2ul3 pic.twitter.com/UCPTCr1Sl7— Mahax (@Mahaximus_) September 7, 2026
Co-Creation: Systems Thinking Beyond the Machine
Complexity thinking is all the rage — in the arts and sciences. Yet, there are two different strands of thinking about complexity, which are often confounded. The first comes from cybernetics, focussing on control in complex situations. The second is ecological, aiming at sustainable participation in a reality beyond control. Their difference rests on a fundamental distinction: is complexity rooted in feedback regulation or collective co-creation? While feedback remains mechanistic, co-creation generates new spaces of possibilities. We need it to understand life and its evolution. And it empowers us to rewrite our future, to escape our mechanistic cage without abandoning scientific rigor. In this paper, we illustrate how we implement these powerful yet abstract principles through our artistic and philosophical practice.
The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits
Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad $\mcT$, capturing this self-similarity. We discuss the algebra $\Rel$ of mathematical relations on $\mcT$, and in so doing use wiring diagrams as a graphical language with which to structure queries on relational databases. We give the example of circuit diagrams as a special case. We move on to show how plug-and-play devices and also recursion can be formulated in the operadic framework as well. Throughout we include many examples and figures.
