PIATRA . INSTITUTE

Morphospace engine

node-graph experiments in the space of possible forms

based on 2019, Levin, The computational boundary of a “self” · 2002, Juarrero, Dynamics in Action

current phenotype

ring shell

6 nodes · 5 edges · evolving

energy

0.53

mean field magnitude

coherence

0.32

spatial organization

e mitigation

0.37

constant containment

platonic depth

0.38

invisible-realm influence

ClaudeApril 2026·Initial implementation

Drag nodes to reposition. Click output port (right) to start a connection, then click input port (left) of target.

t = 0.0

The morphospace hypothesis

Michael Levin proposes that biological form is best understood not as a bottom-up consequence of molecular interactions, but as navigation through a pre-existing space of possible forms — a morphospace. In this view, developmental programs are goal-directed searches through an abstract landscape where attractors correspond to viable anatomies. The morphospace engine takes this idea literally: nodes define forces, tendencies, and constraints that shape a field, and the emergent pattern is a phenotype.

Constraint as cause

Alicia Juarrero argues that constraints are not merely boundary conditions but are causally efficacious. In her framework, enabling constraints create the possibility space within which morphogenesis occurs. A ring constraint in this playground does not merely limit the field — it channels and sculpts it, creating patterns that would not exist without the constraint. This is analogous to how a riverbank does not merely contain water but shapes the flow into meanders, eddies, and deltas.

Mathematical constants as forcing terms

The playground treats mathematical constants ( $e$ , $\pi$ , $\varphi$ , Feigenbaum $\delta$ , silver ratio) as “trans-real” forcing terms — structures from an abstract realm that leave fingerprints on physical morphology when projected into the field. The mitigation parameter controls how much a constraint node absorbs or redirects the constant's influence, while ingress controls how deeply the constant penetrates the field.

\text{push} = s_{\text{eff}} \cdot (1 - m) \cdot \sin\!\bigl(c \cdot (r + \theta) - t\bigr) \cdot G(r)

where $c$ is the constant value, $m$ is mitigation, $s_{\text{eff}}$ is effective strength, and $G(r)$ is a Gaussian envelope.

Node types

Seeds are local generative impulses — point sources of morphogenetic potential with controllable frequency and polarity. Fields distribute tendencies across the whole space along radial, horizontal, vertical, or spiral axes. Constraints channel and dampen the field through ring, stripe, or spiral modes. Constants inject mathematical forcing with controllable mitigation and ingress. Attractors are recursive memory sinks that thicken nascent morphology. Observations probe the field without shaping it.

Emergent phenotypes

The morphology classifier identifies six emergent phenotype classes from the field metrics: spiral membrane (high swirl + coherence), core-focused organoid (center bias dominance), ring shell (edge bias dominance), striped corridor (high anisotropy), amoeboid turbulence (low coherence), and metastable lattice (the balanced default). These are not predefined patterns but categories that emerge from the spatial statistics of the computed field.

Model changelog

v1April 2026

Node-graph architecture with 6 node types: seed, field, constraint, constant, attractor, observation
Field computation on 28×28 grid with Gaussian envelopes, directional fields, and constraint damping
3 presets: e-mitigating moat, Feigenbaum ladder, outside/ingressed
Metrics: energy, coherence, e/δ leakage, center/edge bias, swirl, anisotropy, platonic depth, constraint index
Morphology classification: 6 emergent phenotype classes
Draggable node canvas with SVG edge rendering and real-time field visualization