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Collision-based logic in Lenia and its composition boundary

Chakshu Gupta

arXiv:2609.01348v1cs.ETnlin.CGnlin.PS

TL;DR

Whether a fixed-rule continuous cellular automaton such as Lenia can compute through collisions of emergent patterns remains open. This paper constructs an INHIBIT gate from Orbium glider collisions and tests its composition; the gate blocks across all breathing phases and two gates compose in a single chain.

  • Problem

    Whether Lenia can support logic emerging from glider collisions remains open; prior continuous-CA computation had been trained into the rule rather than produced by such collisions.

    Source: §1 · p. 2

  • Method

    The paper uses an Orbium glider as a signal and a colliding control glider to implement an INHIBIT gate, then composes two gates in series.

    Source: §1 · p. 2, §2.2 · p. 3

  • Results

    Orbium collisions implement an INHIBIT gate that blocks across all phases and nine integer control offsets, and two gates compose into an AND-NOT chain.

    Source: §3.2 · p. 6, §5 · p. 10

  • Takeaways & Limitations

    The immediate open question is whether a deflected signal can be delivered to a downstream gate, the next requirement for composition beyond one straight chain.

    Source: §1 · p. 2

    Beyond the single chain, turned-signal delivery was not demonstrated, and no reusable absorber for surviving gliders was demonstrated.

    Source: §3.3 · p. 6, §3.4 · p. 7

Abstract

from arXiv · show

Continuous cellular automata such as Lenia spontaneously produce lifelike, self-propelling patterns, including the Orbium glider, which travels in a straight line while pulsing through a fixed breathing cycle. Collision-based logic, where moving patterns compute by colliding, is established in discrete cellular automata and continuous physical media. Within continuous cellular automata, computation has so far been trained into the rule rather than emerging from collisions, and whether a fixed-rule automaton like Lenia can support general collision-based computation remains open. This paper constructs an INHIBIT gate from collisions of the Orbium glider. Of the patterns searched across four continuous-CA rule types, the Orbium glider is the only one shown to survive a collision with both copies intact. A control glider deflects a signal glider off its output line, so the output carries a signal only when no control is present. The gate blocks across all twenty-four phases of the breathing cycle and nine integer offsets of the control. Two such gates in series, with one signal line and two controls, compose into an AND-NOT chain, correct on all eight input combinations. By contrast, routing a signal beyond that single chain is undemonstrated. A deflected signal is not restored to a fixed landing position, and no reusable absorber for the surviving gliders was found. The immediate open question for collision-based computation in Lenia therefore narrows from whether a gate exists to whether a deflected signal can be delivered to a downstream gate, the next requirement for composing the gate beyond a single straight chain.

1 Introduction

Mobile patterns make collision-based computing possible in principle, but collision-emergent logic had not been reported in a continuous cellular automaton. This paper constructs an Orbium-based INHIBIT gate and tests how far it composes.

1 Introduction

  • Lenia’s mobile, self-organising patterns provide the travelling localisations that collision-based computing uses to process information where patterns meet [MASH11].The Orbium glider travels in a straight line while pulsing through a fixed breathing cycle.Source: §1 · p. 1
  • Collision-based logic was established in discrete cellular automata and continuous physical media, but not through collisions of emergent patterns in a continuous cellular automaton.In neural cellular automata, logic had instead been trained into the update rule [BFGC25] [MNRM25].Source: §1 · pp. 1–2
  • The paper constructs an Orbium INHIBIT gate: a control deflects the signal off its output track, so the output carries a signal only when no control is present.The gate blocks at every breathing phase across nine integer control offsets; two gates compose into an AND-NOT chain.Source: §1 · p. 2
  • The chain does not demonstrate general circuit composition: delivery of a turned signal to a downstream gate and absorption of surviving gliders remain unresolved.The deflected signal is not restored to a fixed landing position, and no reusable absorber was demonstrated.Source: §1 · p. 2

2 Methods

The methods use Lenia’s Orbium glider as a signal and encode logic in collisions with control gliders. Simulations characterize the glider, specify collision geometry and output measurement, and sweep breathing phase and control offset to identify robust gates.

2 Methods

  • The methods combine the Lenia substrate and Orbium glider with a bit encoding in which glider presence carries a bit and collisions implement logic.The simulation measures collision outcomes and the output bit.Source: §2 · p. 2

2.1 Lenia and the Orbium glider

  • Lenia updates a real-valued field by convolving it with a ring kernel, applying a growth function, scaling by the time step, and clipping the result.Orbium uses a 20 × 20 seed, kernel radius R = 13, and time step dt = 0.1; it travels at 0.603 pixels per step and breathes with a 24-step period.Source: §2.1 · pp. 2–3, Figure 1 · p. 2

2.2 Collisions as logic

  • A signal glider carries 1 by its presence, while a control glider collides with it; a deflected signal reads as 0 at the output window even if it survives elsewhere.The control is a differently headed D4 image; collision outcome depends on impact parameter b and relative breathing phase ϕ.Source: §2.2 · p. 3
  • Candidate phase-stable gates are identified by surveying collision outcomes over impact parameter and breathing phase, then exhaustively sweeping all 24 phases and the chosen integer-offset range.The reported gate uses offsets b = 0 to 13; exact D4 reorientation and Fourier-domain placement are used, and reruns reproduce the counts and windows.Source: §2.2 · p. 3, §2.3 · p. 4

2.3 Simulation and measurement

  • The simulation evolves the field on a periodic grid and classifies interactions from blob counts and total mass; the output bit is measured at a window on the signal’s outgoing track.The reported sweep uses a 361 × 361 grid; analysis code is available at the stated repository.Source: §2.3 · pp. 3–4, Figure 2 · p. 4

3 Results

Orbium collisions yield a phase-dependent set of outcomes, but a perpendicular control can deflect a signal away from its output. Two INHIBIT gates compose correctly in a straight chain; routing beyond it remains undemonstrated.

3.1 The collision as a switch

  • Head-on Orbium collisions produce survival, annihilation, merger, or miss; at b ≤ 20, outcomes usually vary across breathing phases, so b alone does not determine the result.Only two of the 21 columns at b ≤ 20 are phase-uniform, and both show survival.Source: §3.1 · p. 5, Figure 3 · p. 5

3.2 An INHIBIT gate by deflection

  • A perpendicular D4 control deflects the signal off its output, implementing INHIBIT; the gate blocks across all 24 phases at integer offsets b = 0–8, but finer sampling finds leaks near b = 4.The first integer leak is at b = 9; scattered non-integer leaks mean the integer window overstates continuous-placement tolerance.Source: §3.2 · pp. 5–6, Figure 5 · p. 6

3.3 Two gates compose in series

  • Two gates in series produce the correct AND-NOT output for all eight input combinations at four inter-gate spacings, but the chain avoids the survivor-disposal problem of general composition.It emits 1 only when neither control is present, so it never requires disposal of upstream survivors.Source: §3.3 · pp. 6–7

3.4 The composition boundary

  • The gate’s composition boundary is downstream delivery: a turn leaves the surviving signal’s position and heading uncorrected, and no end-to-end turn-to-gate route was tested.The landing spread reaches about 16 pixels at about 70 pixels along one measured route; tolerance to displaced, reoriented input was not measured.Source: §3.4 · p. 7
  • No reusable absorber was found in the searched eater and still-life families, leaving live survivors from deflection without a demonstrated disposal mechanism.Eater annihilation was phase-fragile; the still-life searches yielded no surviving pattern, and other absorber types remain untested.Source: §3.4 · pp. 7–8

3.5 Generality of the deflection prerequisite

  • Only Orbium passed the clean two-glider survival prerequisite among the searched continuous-CA substrates; the other tested species and asymptotic-Lenia glider yielded no clean collision.SmoothLife lacked a vacuum-stable isolated glider to test, while Glaberish collisions were not reproducible, leaving its status undetermined.Source: §3.5 · pp. 8–9, Table 3 · p. 9

4 Discussion

The INHIBIT gate composes only in a straight series chain: turning a signal leaves its position and heading uncorrected, so delivery to another gate remains untested. The discussion identifies signal routing and reusable absorption as the main gaps, while suggesting persistent structures as possible routes forward.

4 Discussion

  • Only series composition is demonstrated; a turned signal’s uncorrected position and heading leave its arrival inside the next gate’s window untested.No reusable absorber for the surviving gliders was found.Source: §4 · pp. 9–10
  • Unlike other collision-computing substrates, Lenia has no demonstrated means of keeping a signal on a known course after collision.Other substrates use lattice quantisation, fixed paths or channels, or soliton restoration pulses and routing.Source: §4 · pp. 9–10
  • Among the standard-Lenia species tested, only Orbium met the deflection prerequisite; unresolved published SmoothLife and Glaberish configurations are not ruled out.The screen is stricter than survival alone, consistent with the reported survival of Orbidae among Lenia’s eighteen soliton families.Source: §4 · p. 10

4.1 Future directions

  • A restoration gadget could return a turned glider to a known position and heading, while persistent structures could potentially restore or absorb gliders.A stationary breathing pattern might reflect or absorb a glider; a reusable catalytic eater would survive the absorption it performs.Source: §4.1 · p. 10
  • The proposed future work also includes a glider-gun constant-one source and testing whether per-stage timing tolerances compose at scale.The period-one fixed-point search could not represent a stationary breathing pattern, and the clean-removal criterion did not test absorber survival.Source: §4.1 · p. 10

5 Conclusion

The paper demonstrates that collisions between Lenia’s emergent Orbium gliders can implement an INHIBIT gate and compose in series. General-circuit composition remains unachieved, with delivery of a turned signal to a downstream gate and reusable absorption still open.

5 Conclusion

  • Orbium collisions implement an emergent INHIBIT gate that is robust to glider breathing, and two gates compose in series.The logic arises from collisions between Lenia’s own patterns rather than being trained into the update rule.Source: §5 · p. 10
  • Only Orbium among the searched configurations was confirmed to provide the enabling collision.Source: §5 · p. 10
  • General-circuit composition remains unachieved because a turned signal’s position and heading are uncorrected, leaving its arrival at a downstream gate untested.Source: §5 · p. 10
  • No reusable absorber was found for the surviving gliders, and the conclusion identifies restoration of a turned glider as a way to keep it on course.The restoration and absorber searches overlap because both concern persistent structures.Source: §5 · p. 10
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