Biology
Ecological Succession
pioneer e^(−kt) → climax 1 − e^(−kt)

Fast-colonizing pioneer species blanket bare ground first, then decline as slow-growing climax species take over; the two curves cross at the point of successional turnover.
Computed & rendered in pure C# on the frozen OnlyCSharp 1.8 library — animation baked to GIF with the library's own
Gif encoder (no GPU, no ffmpeg, no external packages).