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

Alyssa Adams,Hector Zenil,Sara Imari Walker,Paul C W Davies

doi:10.1038/s41598-017-00810-8

Abstract

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 isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we implement novel variants of cellular automata (CA) where 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, 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.

Highlights

Many real-world biological and technological systems display rich dynamics, often leading to increasing complexity over time that appears to be limited only by availability of resources
The vast majority of executions sampled from all three cellular automata (CA) variants were innovative by Definition 2, with > 99% of Case II and Case III CAs displaying INN, such that their dynamics are not captured in the trajectory of states for any isolated Elementary Cellular Automata (ECA) with a fixed rule of width w = wo
We have provided formal definitions of unbounded evolution (UE) and innovation (INN) that can be evaluated in any dynamical system which can be decomposed into two interacting subsystems o and e

Summary

Introduction

Many real-world biological and technological systems display rich dynamics, often leading to increasing complexity over time that appears to be limited only by availability of resources. Many working definitions exist, which can be classified into four hallmark categories as outlined by Banzhaf et al [8]: (1) on-going innovation and generation of novelty [9, 10]; (2) unbounded evolution [1, 11, 12]; (3) on-going production of complexity [13,14,15]; (4) a defining feature of life [16] Each of these faces its own challenges, as each is cast in terms of ambiguous concepts. Processes may appear unbounded, even within a finite space if they can continually produce novelty within observable dynamical timescales [17]

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