🌀 nonlinear sciences

Collision-based logic in Lenia and its composition boundary

This paper demonstrates the construction of a functional INHIBIT gate and a two-stage AND-NOT chain using collisions of Orbium gliders in Lenia, establishing that collision-based logic is possible in continuous cellular automata while highlighting the remaining challenge of reliably routing deflected signals to downstream gates.

Original authors: Chakshu Gupta

Published 2026-09-02

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Chakshu Gupta

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast landscape of computing, there is a quiet corner where machines do not rely on silicon chips or electrical wires, but on the simple, self-organizing behavior of patterns. Imagine a grid of cells, each holding a value that can change over time, much like a pixel on a screen that brightens or dims based on its neighbors. In a specific type of digital universe known as a continuous cellular automaton, these cells do not just switch on and off; they flow like a fluid, creating shapes that move, breathe, and repair themselves. Among these shapes are gliders, tiny, self-propelling structures that travel in straight lines, pulsing with an internal rhythm as they cross the grid. For decades, scientists have wondered if these moving patterns could do more than just exist; they asked if these gliders could collide with one another to perform calculations, acting as the building blocks of a computer where information is carried by the movement of the patterns themselves. This idea, known as collision-based computing, has been proven to work in other digital systems and even in real-world chemical reactions, but it remained an open question whether it could emerge naturally in the fluid, continuous world of Lenia.

A researcher at the Georgia Institute of Technology set out to answer this question by treating the Lenia grid as a laboratory for logic. The goal was to see if two of these moving gliders could crash into each other in a way that produces a predictable result, effectively creating a switch that turns a signal on or off. The scientist focused on a specific glider called the Orbium, a stable, breathing shape that travels in a straight line. By carefully arranging for a second glider to cross the path of the first, the researcher tested whether the collision could block the signal or let it pass. The experiment involved simulating thousands of crashes, varying the exact timing of the collision and the angle at which the gliders met. The results showed that it is indeed possible to build a logic gate, a fundamental component of computing, using these collisions. Specifically, the researcher constructed an INHIBIT gate, a device that allows a signal to pass only if a second, controlling signal is absent. When the control glider was present, it deflected the signal glider off its course, preventing it from reaching the destination. When the control was absent, the signal glider continued straight through, successfully reaching the output.

This success, however, came with a specific and narrow set of conditions. The collision had to be precise; the control glider had to hit the signal at a very specific distance from its center, a margin of error of only about four pixels. Furthermore, the gate had to work regardless of the exact moment in the glider's breathing cycle when the crash occurred. The researcher found that the gate held up across nine different positions and every single phase of the glider's 24-step breathing rhythm, proving that the logic is robust against the natural fluctuations of the moving pattern. To test how far this logic could go, the researcher placed two of these gates in a row, creating a chain where a signal could be blocked by either of two controls. This chain worked perfectly, correctly processing all possible combinations of inputs. Yet, this success revealed the limits of the system. While the gates could be linked in a straight line, the system could not yet be arranged into a complex circuit. The main obstacle was that when a glider was deflected by a collision, it did not land in a predictable spot or face a predictable direction. In a full computer, a signal must be able to turn corners and be delivered precisely to the next gate, but in this simulation, the deflected glider drifted, its final position and angle varying too much to be reliably caught by a downstream device.

The study also investigated whether these surviving gliders could be cleaned up after a collision, a necessary step for reusing the space in a complex circuit. The researcher searched for a way to absorb the extra gliders that remained after a deflection, looking for a pattern that could act as a trash collector. After testing various shapes and collision angles, no reusable absorber was found. Some collisions destroyed the gliders, but only under very specific, fragile timing conditions that would fail if the timing shifted even slightly. Others simply failed to remove the extra mass. Without a way to reliably clear the path of these survivors, or a way to steer a deflected signal back onto a fixed track, the construction of a general-purpose computer using these collisions remains out of reach. The paper concludes that while the basic building block exists, the machinery needed to connect them into a larger system is missing. The question has shifted from whether such a gate can exist, which is now confirmed, to whether the deflected signals can be delivered to the next gate with the precision required for a working circuit. Until a method is found to restore the position and direction of a turned glider, or to absorb the survivors, the dream of a computer built entirely from colliding, breathing patterns in Lenia remains a possibility that has not yet been realized.

Technical Summary: Collision-based Logic in Lenia and its Composition Boundary

Problem Statement
Continuous cellular automata (CA) like Lenia spontaneously generate lifelike, self-propelling patterns, such as the Orbium glider. While collision-based computing—where information is processed via the interaction of moving localizations—is well-established in discrete CAs (e.g., Rule 110) and continuous physical media (e.g., Belousov–Zhabotinsky reactions), it remains unproven in continuous CAs with fixed update rules. Previous work in neural CAs has achieved computation by training logic into the update rule via gradient descent, but this paper investigates whether general collision-based computation can emerge from fixed-rule interactions. The central question is whether a fixed-rule automaton like Lenia can support logic gates formed by colliding gliders, and if so, whether these gates can be composed into complex circuits.

Methodology
The study utilizes the standard Lenia substrate with the Orbium glider as the signal carrier. The methodology involves:

Simulation: A double-precision simulation on a periodic square grid evolves the real-valued field $A \in [0, 1]$ . The update rule involves convolving the field with a radial kernel $K$ to generate a potential $U$ , applying a growth function $G(U)$ , and clipping the result.
Logic Encoding: A logic bit is encoded by the presence (1) or absence (0) of a glider on a specific trajectory. A logic gate is formed by the collision of a "signal" glider ( $S$ ) and a "control" glider ( $C$ ). The control is a $D_4$ symmetry image (rotation/reflection) of the signal.
Collision Analysis: The outcome of collisions is classified based on the final field mass and the number of connected "blobs" (regions where $A > 0.10$ ). Outcomes include annihilation, explosion, merger, survival, or miss.
Gate Construction: The author searches for a geometry where a control glider deflects a signal glider off its output track without destroying either. The output is read at a fixed window on the signal's original trajectory.
Robustness Testing: The system is tested across all 24 phases of the Orbium glider's internal breathing cycle and various integer impact parameters ( $b$ ) to ensure phase stability.
Composition and Prerequisite Testing: The author tests the series composition of gates and survey four different continuous-CA rule types (Standard Lenia, Asymptotic Lenia, SmoothLife, Glaberish) to determine if the "deflection prerequisite" (surviving collision with both gliders intact) is general or unique to Orbium.

Key Contributions and Results

Construction of an INHIBIT Gate: The paper successfully constructs an INHIBIT gate ( $out = S \land \neg C$ ) using Orbium gliders. In this configuration, a control glider crosses the signal's path perpendicularly. If the control is present, it deflects the signal off the output track (output 0); if absent, the signal passes straight through (output 1).
Phase Robustness: The gate is robust across all 24 phases of the glider's breathing cycle. It functions correctly for nine integer impact offsets ( $b = 0$ to $8$). The gate blocks the signal in 89% of the tested points within the range $b=0$ to $13$, though finer sweeps reveal leaks at non-integer offsets.
Series Composition: Two such gates can be composed in series to form an AND-NOT chain ( $out = S \land \neg C_1 \land \neg C_2$ ). This chain produces correct outputs for all eight input combinations. Crucially, this specific composition works because the chain only outputs a "1" when no controls are present, meaning no "surviving deflected gliders" need to be disposed of within the chain itself.
Composition Boundary: The paper identifies a hard limit in composing these gates beyond a single straight chain. Two capabilities required for general circuits remain undemonstrated:
1. Delivery: A deflected signal is not restored to a fixed position or heading. The exit heading has a circular standard deviation of 8–14°, and the landing point spreads by approximately 16 pixels over a 70-pixel downstream distance. No "restoration gadget" (reflector or waveguide) was found to correct this.
2. Disposal: No reusable absorber was found to clear the surviving deflected gliders that would otherwise clutter a general circuit. Searches for "mutual-annihilation eaters" and "static still-lifes" yielded no phase-robust or reusable solutions.
Generality of the Deflection Prerequisite: A survey of four continuous-CA rule types and ten other Lenia species revealed that Orbium is the only pattern shown to survive a collision with both copies intact. Other species either lose coherence, fail to form isolated gliders, or produce non-reproducible collisions (e.g., Glaberish).

Significance and Claims
The paper claims that while a functional logic gate exists in Lenia, the system currently cannot support general-purpose collision-based computation. The significance of the work lies in narrowing the open question: the existence of a gate is no longer the barrier; the barrier is the delivery of a deflected signal to a downstream gate and the disposal of collision survivors.

The author explicitly states they do not claim to have built a working computer, nor do they prove that Lenia cannot host one. Instead, they demonstrate that the immediate obstacle is the lack of mechanisms to correct the position/heading of deflected signals and to absorb survivors. The paper concludes that while the "encoding" (presence of a glider) works, the "routing" (keeping the value on a known course after interaction) remains unproven in free-space Lenia, distinguishing it from other substrates where signals are confined to fixed paths or actively restored.

Technical Summary: Collision-based Logic in Lenia and its Composition Boundary

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