# Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems

arXiv: https://arxiv.org/abs/1607.01750 · HTML: https://mlsanity.com/paper/1607.01750/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2016.

## Built on by (most cited first, 6 of 6)

- [Self-Replication, Spontaneous Mutations, and Exponential Genetic Drift in Neural Cellular Automata](https://mlsanity.com/paper/2305.13043/) (2023)
- [Multiclass classification utilising an estimated algorithmic probability prior](https://mlsanity.com/paper/2212.07426/) (2022)
- [PEPA: a Persistently Autonomous Embodied Agent with Personalities](https://mlsanity.com/paper/2603.00117/) (2026)
- [Emergence in artificial life](https://mlsanity.com/paper/2105.03216/) (2021)
- [The use of knowledge in open-ended systems](https://mlsanity.com/paper/2412.00011/) (2024)
- [Intrinsic Motivation in Reinforcement Learning: A Research Agenda for Adaptive Self-Organisation](https://mlsanity.com/paper/2609.17325/) (2026)

## Abstract (arXiv)

Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in biology. We recast the problem as a more general one in dynamical systems theory, providing simple criteria for open-ended evolution based on two hallmark features: unbounded evolution and innovation. We define unbounded evolution as patterns that are non-repeating within the expected Poincare recurrence time of an equivalent isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we implement novel variants of cellular automata (CA) in which the update rules are allowed to vary with time in three alternative ways. Each is capable of generating conditions for open-ended evolution, but vary in their ability to do so. We find that state-dependent dynamics, widely regarded as a hallmark of life, statistically out-performs other candidate mechanisms, and is the only mechanism to produce open-ended evolution in a scalable manner, essential to the notion of ongoing evolution. This analysis suggests a new framework for unifying mechanisms for generating OEE with features distinctive to life and its artifacts, with broad applicability to biological and artificial systems.