A fractal vise will clamp a spanner, a walnut and a hex bolt in the same bite, press on all three with near-equal force, and do it without a single spring, sensor or drop of hydraulic fluid. The whole trick is a tree. Each jaw is not one face but a nested stack of semicircular segments. One large arc pivots on the jaw body. Riding in a dovetailed groove cut into that arc are two smaller arcs, each free to rotate. Each of those carries two smaller ones again. Three levels of nesting gives eight independent contact fingers per jaw; four levels gives sixteen. What matters is what happens at every pivot. A freely rotating segment cannot transmit a moment about its own pin. It can only settle where the loads from its two children balance. That makes every pivot a small balance beam, and the whole jaw a binary force-splitting network: - The screw applies one load to the top arc - That arc rotates until its two children see equal force - Each child does the same for its own pair - Eight fi...