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warp the surface / mathematics

boundary conditions

create / explore / learn

A precise family of curves appears to be the artwork. In fact, every interior line is only the necessary consequence of fixed values placed around the edge.

Activate points around the boundary to cycle them between neutral, high, and low. Never draw inside the field. Let the interior relax, then compare the contours with the gradient flow underneath them.

change only the edge · the interior must answer

Five fixed edge values determine the first harmonic field. Activate any boundary point to change a condition; the interior cannot be edited directly.

felt

Changing one fixed value at the edge reorganized curves throughout the interior. The field visibly relaxed toward a new solution even though you never touched a contour.

found

The drawing is a harmonic solution to boundary conditions. Interior values repeatedly average their neighbors toward ∇²φ = 0, and the visible curves are equipotential contours extracted from that scalar field.

carry

Many outcomes are authored indirectly. Interfaces, structures, policies, physical systems, and optimization problems can be changed more powerfully by changing their boundary conditions than by editing each result individually.