FR21 · Growth and dilution
What happens to a chemical pattern when its domain expands? Growth stretches the available wavelengths and dilutes each substance over a larger area. Even when the total amount stays constant, concentration falls, which changes the reaction and the pattern.
Expand the same patterned square and watch old peaks stretch and new ones emerge. Compare concentration with total amount, then turn reactions off to isolate dilution.
SIMULATION RECORD AND ANALYTIC REFERENCE
Cyan: mean activator concentration relative to the prepared state. Gold: total activator amount relative to that state. Reactions can change total amount; switch to Conserved amount to remove both source and sink.
The field uses one fixed color scale: dark blue at zero, cyan near one and amber at 2.5 and above. Opposite edges touch.
Physics tutorial
BackgroundWhen the patterned material expands, neighboring material points move apart. The same chemical amount occupies more area, so its concentration falls unless reactions replace it.
Why it mattersChanging the picture size alone misses this dilution. Following the material lets us keep track of diffusion, chemical production and the growing area together.
Start with the essentials
The material coordinates remain fixed as the physical square grows. Length and time are dimensionless, and the growth rate is the fractional increase of side length per unit time.
The factor of two comes from growth in two directions. The substrate has the same dilution term, with its own diffusivity and reaction rate.
Periodic diffusion transfers material internally. With all reactions off, the total amount remains constant even though concentration changes.
Typical misconceptionA falling concentration means the chemical has disappeared.
Better mental modelAn expanding area can lower concentration without removing any molecules. Multiply mean concentration by the current area to calculate total amount.
Typical misconceptionThe same reaction parameters should preserve the original mean concentration.
Better mental modelGrowth continuously dilutes both species. Their reaction rates respond to the new concentrations, and the combined balance can move away from the fixed-domain equilibrium.
Start with Growing pattern and compare the cyan and gold curves.
What to observe: Concentration and total amount follow different histories because the area is changing and reactions continue.Select Conserved amount.
What to observe: The gold curve stays at one. The cyan curve decreases as the square expands; all of this decrease comes from dilution.Select Fixed domain, then compare with Fast expansion.
What to observe: The fixed domain retains its original physical spacing. Growth stretches the old pattern and changes which physical wavelengths fit inside the square.Morphogenesis and reaction–diffusion · Reading path
Articles on this path that use this experiment, followed by the other experiments they suggest.