Engineering
Transient Heat Diffusion
T(x,t) = e^(−t)·sin(πx)
A rod held cold at both ends: the fundamental temperature mode keeps its sinusoidal shape while its amplitude bleeds away exponentially as heat conducts out.
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).