The embryo is drawn as a short tube of cells (a cross-section through an early embryo). A morphogen — a diffusible signalling protein — is secreted continuously at one line running the length of the tube (the ventral midline, as with the transcription factor Dorsal in the fruit fly embryo). It spreads around the circumference by diffusion while decaying, so a real concentration gradient builds up and reaches a steady shape rather than appearing instantly.
∂C/∂θ,t = D·∇²C − k·C (+ continuous secretion at θ=0)
fate(cell) = mesoderm if C+noise > T_hi
= neuroectoderm if T_lo < C+noise ≤ T_hi
= ectoderm otherwise
inward(cell) → target_depth(fate), relaxed each frame
- Secretion strength — how much morphogen the ventral source produces; higher values push the whole gradient up and recruit more cells past each threshold.
- Diffusion rate — how fast the signal spreads around the circumference; low values keep a sharp spike near the source, high values flatten the gradient across the whole embryo.
- Decay rate — how quickly the morphogen is degraded; this sets how far from the source the signal can still be read before it fades to noise.
- Cell noise — per-cell stochastic variation in how a fixed concentration is interpreted, illustrating why real fate boundaries are never perfectly sharp (a "salt-and-pepper" effect) even from a smooth gradient.
- Fate thresholds — the two concentration cutoffs that split one continuous gradient into three discrete fates, the core idea of Lewis Wolpert's "French Flag" positional-information model.
- Invagination speed — once committed, mesoderm cells change shape and pull inward, folding the sheet into a groove (the ventral furrow) — the first movement of gastrulation, driven directly by the fate a cell was assigned.
Real-world relevance: this is a simplified, interactive version of dorsoventral patterning in the early Drosophila embryo, where a single nuclear gradient of the Dorsal protein specifies mesoderm, neuroectoderm and dorsal ectoderm in concentric bands, and the highest-concentration band alone triggers the cell-shape changes that begin gastrulation.