Metamorphosis · field

One grid.
Three functions.
A living boundary.

The same set of points. Two phase-sources orbit the field, and every node samples a local phase from both. So one region flows blue, another crosses gold, a third bursts orange — and the boundaries between them drift, breathe, and never cut the line.

dominant
—
calm region
—
reaction region
—
turning region
—
the phase is a geography
Two sources orbit the grid — hover to halve their speed. Each node's phase blends from both by distance, so the three functions coexist at once. The lines move, but the strands never break.
Phase field

Where the original traced a single phase across the whole grid, this field gives every node its own local phase. The Gaussian weights — one at 0, one at 0.5, one at 1, summed to unity — still decide all three functions at once. The boundary is not drawn; it emerges from the geometry.

Three arrangements
calm
Wave · flows
Horizontal strands, blue, continuous — where the local phase sits near 0.
fn[n]
Grid · crosses
Diagonal structure, gold — where the phase sits near the reaction at 0.5.
turning
Burst · diverges
Radial to center, orange — where the phase approaches 1.
Not one function that becomes another — a field where all three are true at once, in different places, forever in motion. The boundary is not a line. It is a weather.