cs.NEMar 9, 2026
SaveEvolving Symbiosis, from Barricelli's Legacy to Collective Intelligence: a simulated and conceptual approach
Organizations: Independent Researcher, Oxford, UK · Inria Center at the University of Bordeaux, Bordeaux, France · University of Copenhagen, Copenhagen, Denmark · University of Trieste, Trieste, Italy ·
Abstract
This report documents the work of our group (named SymBa) at the ALICE 2026 workshop in Copenhagen. Inspired by the pioneering work by Nils Aall Barricelli on symbiogenesis of numerical organisms (i.e., 1D cellular automata) in 1953 (70+ years ago!!), we discussed the role of symbiogenesis as mechanism contributing to the origins of life, open-endedness, and collective intelligence. We report replications of Barricelli's original work in 1D worlds, an extension to 2D symbioorganisms, and preliminary experimentation with DNA-norms. We discuss the implications of symbiogenesis for artifical life and artificial intelligence, and outline several opportunities for future works, both at the conceptual level as well as using different substrates (neural networks, neural cellular automata, etc.)
Figures & tables
Figure 1: Extract from original paper by Barricelli published in Italian ( Barricelli, 1954a ) .
Figure 2: An emergent symbioorganism from Barricelli’s work.
Figure 3: Example of symbiotic interactions causing mutiple replications that would not have happened without symbiosis.
Figure 4: Example of emergent crossover.
Figure 5: Example of emergent crossover.
Figure 6: Example of DNA norms proposed by Barricelli.
Figure 7: Example of evolutionary computation and embodiement proposed by Barricelli.
Figure 8: Barricelli’s numerical system. On the top, an example of a single number replication. In the bottom, the number 4 is replicated twice, due to interaction with the number -3.
| Name of the norm | -value (computed by mutation or exclusion) | Conditions |
|---|---|---|
| Norm 0 | Collision of different genes. | |
| Norm A | Collision under empty cell if and have same sign. | |
| Same collision if the sign is not the same. | ||
| Collision under occupied cell. | ||
| Norm B | Respectively same conditions as in A norms. | |
Table 1: Barricelli’s collision norms.
Figure 9: Barricelli’s symbioorganism.
Figure 10: Barricelli’s reports on large scale experiments. Left: Barricelli system initialized with random numbers converges towards symbioorganisms. Reproduced from Figure 15 of ( Barricelli, 1962a ) . Right: Barricelli system with heterogeneous norms, annotations demarcate different norms and symbioorganisms. Reproduced from Figure 9 of ( Barricelli, 1957a ) .
Figure 11: 6 examples of Barricelli’s numerical systems with norm and periodic boundary conditions. The grid of length 256 is initialized with 10 random numbers in the center, the rest are 0. The simulations ran for 512 generations.
Figure 12: Barricelli’s norm executed on a environment, with an 80% sparse initialization and toroidal wrapping. Each point represent the vector at that position by calculating it’s polar angle with and applying a divergent color scheme. A video of the full run is available here .
Figure 13: DNA norms used in our implementation.
Figure 14: Simple metrics computed for sparse and dense initial conditions over 256 timesteps. The experiments use periodic boundary conditions and norm. Top row: Spatiotemporal evolution of the 1D world. Middle row: Aggregate population dynamics showing total replication candidates and living (non-zero) cells over time. Dense initial conditions exhibit rapid population collapse following regrowth, while sparse conditions show gradual population growth as organisms spread into empty space. Bottom row: Log-scale distribution of cell values over time, revealing which (numerical values) dominate. Under norm, organisms attempting to replicate into occupied cells mutually annihilate, creating strong selection pressure favouring spatial strategies that minimise conflict.
Figure 15: Information metrics for a Barricelli automata over time. The ‘mutual information‘ is calculated pairwise between all time-steps, and the ‘Shannon entropy‘ is calculated for individual time-steps.
Figure 16: A visualization of how one might study the robustness of Barricelli’s symbioorganisms. The grids are initialised with the symbioorganism in the centre. A single additional cell is initialised with a non-zero number that eventually collides with the symbioorganism.
Figure 17: An example Boolean symbiogenesis. Left: from random initial state; Right: detailed view.
Figure 18: Motif repetition across runs. For each cycle and motif length , we measure the fraction of length- windows that correspond to motifs observed more than once in the population. A run is counted as positive if (here ). Curves show , the fraction of independent runs meeting this criterion, comparing Condition A (elongation-only; green) and Condition B (full DNA norms; blue). Shaded regions indicate 95% Wilson confidence intervals.
Figure 19: Spatial signature of DNA-norms in a 1D cellular automaton. Spacetime diagrams (space on , cycle on ) show the dominant -mer identity per cell at each cycle for elongation-only (Condition A; panels A–C) and full DNA-norms with complementary association/overlap-mediated merging and splitting (Condition B; panels D–F). Columns correspond to motif length . Colors indicate the most frequent -mers (legend in each panel); gray denotes no assignment to the displayed top set. Under Condition A, dominance appears primarily as sparse, short-lived streaks that rarely spread, becoming increasingly rare with larger . Under Condition B, dominant motifs form contiguous cone-shaped domains that expand from nucleation sites and persist over many cycles, remaining detectable even at .