Cellular Tissue

Picture a grid in which each site belongs to a cell or to medium. The tissue evolves not by smooth PDE flow but by countless small proposals: copy one site’s identity onto a neighbour and ask whether the move lowers an energy. Contacts between cell types have costs; cells prefer certain areas and perimeters. At finite temperature, uphill moves sometimes occur, so the tissue can explore rearrangements. From that microscopic gambling emerges macroscopic behaviour—sorting into domains, tense boundaries, wound closure and chemotactic drift—without any cell containing a drawing of the final pattern.

The Cellular Potts Model (also called the Glazier–Graner–Hogeweg model in broader usage) represents cells as extended domains on a lattice. A Monte Carlo sweep (MCS) proposes copy attempts. For an energy change (\Delta H), the Metropolis rule accepts the copy with probability (1) if (\Delta H\le 0) and with probability (\mathrm{e}^{-\Delta H/T}) if (\Delta H>0).

Typical Hamiltonian pieces include:

• Contact energy from a type–type matrix (including medium);
• Area constraint pulling each cell toward a target area;
• Perimeter / shape terms penalising excess boundary or wrong compactness.

Pack Tissue V2 implements this family (modelVersion: 2): metropolisAttempt() accumulates local contact, area and perimeter contributions; mcsPerSecond converts wall time into MCS sweeps; optional chemotaxis, polarity and growth/division extend scenarios beyond pure sorting.

Simple surface honesty

ecospheres.ai’s simple controls are:

• Temperature — Metropolis (T)
• MCS / second — physics pace
• Membrane strength, Nucleus strength, Field overlay — largely visual emphasis for contours, nuclei and morphogen tint

The pack’s own default simple profile still lists affinity and softness first, and every preset carries those values. Ecospheres deliberately overrides that profile: affinity/softness are not on the public simple dock. Do not teach visitors that moving a hidden affinity slider is part of the public lesson. Contact matrices and constraints remain editable in advanced/lab contexts and in presets.

Contours versus physics clocks

Contour extraction for rendering runs on the order of ~30 Hz. Physics advances in MCS according to mcsPerSecond. Smooth membrane lines can therefore look continuous while the underlying copy attempts are discrete and stochastic. Teach visitors to respect both clocks.

Differential adhesion hypotheses (Steinberg) proposed that cell sorting reflects adhesive preferences. Graner and Glazier’s Cellular Potts Model gave a lattice energy framework in which contact energies and constraints produce sorting, rounding and tissue-scale rearrangement. The model became a workhorse of computational morphogenesis and collective cell behaviour, later extended with chemotaxis, polarity and proliferation.

ecospheres.ai’s Cellular Tissue sphere presents that modelling tradition interactively. It is not a claim that a particular embryo or epithelium has been parameter-fitted.

Aspect	Current implementation
Model	CPM V2 (Glazier–Graner lineage); V1 path disabled for shipping.
State	Lattice cellId domains; types; optional morphogen field.
Dynamics	Metropolis copy attempts; MCS sweeps paced by mcsPerSecond.
Energy	Contact matrix + area + perimeter/shape terms; extensions for activity/chemotaxis/growth in scenarios.
Temperature	Metropolis (T) on the simple surface.
Visuals	Membrane/nucleus/field overlay strengths; contour extract ~30 Hz.
Pack default simple knobs	Pack profile still lists affinity and softness first; ecospheres overrides them off the public dock.
Public simple controls	Temperature, MCS/second, Membrane, Nucleus, Field overlay.
Public simple tools	Spawn, Brush, Erase with Wound / Morphogen / Type / Divide targets.
Showcase	Wound Closure (preset index 2) on desktop and mobile.
Secondary literacy preset	Sorting Embryo at mcsPerSecond: 72.
Hero framing	Host observer camera enabled (Reset view); presentation-only. Contours remain a ~30 Hz render layer.

The most truthful one-line description is: a Cellular Potts tissue whose cells rearrange by Metropolis energy minimisation on a lattice.

Sorting without a blueprint

In Sorting Embryo, mixed types should demix into domains. The contact matrix—not a painted target map—is doing the work.

Boundary tension

Boundary Tension makes interfaces readable. Look for smooth versus interdigitated contacts as temperature and constraints change.

Wound closure

Showcase Wound Closure: a gap in a monolayer and the tissue’s attempt to close it, with chemotaxis/injury morphogen participating in the scenario. Closure is emergent from copy attempts and energies, not a wipe animation.

Temperature as boldness

High (T) accepts more uphill moves—fluid, noisy tissue. Low (T) looks more greedy and can freeze into jammed configurations.

MCS pace versus contour smoothness

Raise MCS/second and the physics races; contours still refresh on their render cadence. Do not mistake silky outlines for continuous PDE membranes.

Membrane and nucleus as lenses

These sliders emphasise drawings of boundaries and centres. Treat them as microscopes, not adhesion coefficients—especially because affinity/softness are not on the simple dock.

First 30 seconds

1. Load showcase Wound Closure.
2. Identify the wound and watch copy-driven closure attempts.
3. Lower Temperature and note whether motion becomes more decisive or stuck.
4. Load Sorting Embryo (72 MCS/s) and watch demixing.
5. Brush Wound into a sorted domain; compare recovery with the showcase scenario.
6. Dim Field overlay to separate morphogen tint from cell IDs.

Three experiments

Experiment	Question	Do	Watch for	Why it matters
Adhesion sorts	Do types unmix without a drawing?	Sorting Embryo → wait through MCS.	Domain formation by type.	Classic CPM lesson.
Thermal exploration	What does temperature mean here?	Wound Closure → sweep Temperature.	Fluid rearrangement vs frozen scar.	Metropolis (T), not body heat.
Intervention	Can a local edit rewrite tissue fate?	Brush Wound or Change type → wait.	Recoil, closure or new boundary.	Energy dynamics respond to geometry.

Parameter	What it really controls	Increase it	Decrease it	What to watch
Temperature	Metropolis acceptance of uphill (\Delta H).	More exploratory, fluid tissue.	Greedier, possibly jammed tissue.	Sorting quality and wound motion.
MCS / second	How fast Monte Carlo sweeps accrue.	Faster physics.	Slower, more readable steps.	Pace ≠ contour refresh rate.
Membrane strength	Visual contour emphasis.	Stronger outlines.	Softer drawing.	Presentation only.
Nucleus strength	Visual nucleus markers.	Stronger centres.	Less nuclear ink.	Presentation only.
Field overlay	Morphogen tint strength.	Stronger field read.	Cells-only view.	Mostly visual on simple surface.
Affinity / softness (pack, not eco simple)	Pack-level adhesion/compliance compressions.	N/A on public simple dock.	N/A.	Mention honestly as advanced/pack-only.
Contact matrix / area / perimeter (advanced)	True CPM energy knobs.	Retunes sorting and shapes.	Retunes opposite.	Scientific core behind presets.

The best first pair is Temperature and MCS / second: one sets stochastic boldness, the other sets how quickly that boldness is sampled.

Sorting Embryo

Secondary literacy preset at 72 MCS/s. Fast demixing classroom; not the showcase because high MCS can feel hurried for first-time visitors.

Boundary Tension

Two-tissue interface laboratory for reading contact energies as boundaries.

Wound Closure

Showcase on desktop and mobile. Clearest public narrative: injury, collective motion, closure attempt.

Chemotactic March

Directed migration under chemotaxis strength/morphogen scenario—teach as CPM + field coupling, not as animal taxis documentary.

Growing Epithelium

Division/growth parameters enter; proliferation joins adhesion.

Contact Memory

Slower MCS (30/s) and memory-themed contacts—editorial regime, still CPM underneath.

Recommended learning order: Wound Closure → Sorting Embryo → Boundary Tension → Chemotactic March → Growing Epithelium → Contact Memory.

• Spawn adds cellular material / agents according to tissue spawn semantics.
• Brush → Wound clears or injures tissue locally.
• Brush → Add morphogen paints morphogen field.
• Brush → Change type retypes cells in the brush.
• Brush → Divide triggers division-related intervention where scenario allows.
• Erase removes lattice occupancy in the brush.

No field actions are exposed on the ecospheres simple surface for tissue.

Cells are lattice domains with energies, not wet biological cells with membranes, nuclei genomes or biochemistry—even when nuclei are drawn.

Membrane and nucleus sliders are visual. Affinity and softness are not on the simple ecospheres surface; do not imply visitors were tuning them.

Contour smoothness is not the MCS clock.

Wound closure is not clinical healing.

Sorting Embryo is not a claim of a fitted developmental dataset.

Temperature is Metropolis (T), not Celsius.

The defensible conclusion is:

When extended cells rearrange by energy-minimising copy attempts, adhesion preferences and shape constraints become tissue-scale behaviours—sorting, boundaries and wound response—without a global drawing of the outcome.

Cellular Tissue adds energy-driven multicellular rearrangement to the atlas. Neural Morphogenesis grows pattern with a learned local net; Lenia sustains continuous animals; Tissue shows another classical route from local rules to form: differential adhesion and constraints under Monte Carlo dynamics. It is the natural Life-domain counterpart to questions of sorting, interface tension and collective repair.

Foundational and primary sources

1. François Graner and James A. Glazier, “Simulation of biological cell sorting using a two-dimensional extended Potts model,” Physical Review Letters 69(13), 2013–2016 (1992). DOI: 10.1103/PhysRevLett.69.2013. Foundational CPM / extended Potts cell-sorting paper.
2. James A. Glazier and François Graner, “Simulation of the differential adhesion driven rearrangement of biological cells,” Physical Review E 47(3), 2128–2154 (1993). DOI: 10.1103/PhysRevE.47.2128. Expanded CPM treatment.
3. Broader CPM / GGHH modelling reviews and textbooks in computational morphogenesis for contact energy, area/perimeter constraints and MCS semantics (lineage context; the engine is V2 Potts tissue, not a single review’s code).