Cream = dough, yellow = butter. Layers are drawn the same thickness (toy picture).
Tap the buttons in order (or tap the tools in the kitchen).
Inside the pastry: steam (blue) pushes the layers apart.
Layers by folding. Puff pastry is dough with a block of butter wrapped inside. Each time you roll it out and fold it, the number of butter layers is multiplied: a book fold (in half) multiplies by 2 and a letter fold (in thirds) multiplies by 3. After n letter folds the butter makes L = 3n layers, with dough layers in between, so there are 2L + 1 layers in total. Rolling keeps the volume, so the sheet thickness stays about 6 mm and each layer gets thinner: layer = 6 mm / (2L+1).
Warm or cold butter. If the butter is warm (above about 18 °C) it smears into the dough and layers merge. If it is too cold (below about 8 °C) it is brittle and tears the dough, and steam later leaks out. In the toy model each fold smears with chance s = 1/(1+e-(T-21)/2) so the intact fraction is (1-s)n, and tears reduce the steam by up to 70%.
Steam pushes layers apart. The water in dough and butter turns to steam. Water vapour pressure rises quickly with temperature. We use the Antoine equation log10P = A - B/(C+T) (P in mmHg, T in °C) and check it against the Clausius-Clapeyron equation P = P0 exp[-(LvM/R)(1/T - 1/T0)]. At 100 °C both give about 101.3 kPa, the air pressure around us. Above 100 °C the extra pressure ΔP = Psat - 101.3 kPa can lift a layer.
Gap and rise. A dough layer acts like a springy skin. In the model the gap it opens is g = gmax ΔP / (ΔP + σ), where σ is the dough springiness. Every butter layer becomes one gap, so total height is H = t + Leff × g. More layers, more rise. The pastry stops rising when the dough dries and sets.
Browning. The golden colour comes from the Maillard reaction, whose speed grows quickly with temperature (Arrhenius law). Egg wash adds protein and speeds it up. Too cool: pale. Too long: dark.
Honest simplifications. One temperature for the whole pastry, no heat gradients, no butter leaking out, layers all equal, constants chosen to look like a real tree (about 6 to 8 times taller with 700 layers). The numbers show the idea, they are not measurements of one recipe. Not affiliated with any brand.
Checks. We count layers by really folding a list and compare with the formula; compare Antoine and Clausius-Clapeyron; and compare total rise with layers times gap.