鋼球が延々と模様を描くキネティック・サンドテーブル

Build a kinetic sand table simulation in a single self-contained HTML file. Show a round tray of fine sand inside a dark wooden rim, seen from above with soft lighting. A small steel ball rolls across the sand and carves a groove that remembers every pass; there is no eraser, so each new pattern is drawn over the previous one and the old design slowly smooths away into the next. Generate an endless sequence of mathematical patterns that never repeat, such as spirals, rose and flower curves and Lissajous figures, and show the current pattern name in a small caption. Add a minimal control bar with play, pause and skip, and a counter for the number of patterns drawn. Use warm sand tones with subtle grain and shading on the groove edges. Done means the groove looks believable, patterns blend smoothly into each other and the piece can run unattended.