Rectangular strip of the hyperbolic plane in 3-space, with geodesic spreading visible as buckling
A rectangular strip of the hyperbolic plane with metric ds2=dx2+cosh2(x)dy2 is discretized into a mesh and embedded into R3 using a spring network. Each spring’s rest length encodes the intrinsic hyperbolic distance between adjacent vertices, and electric charges on vertices provide a repulsive force to prevent self-intersection.
The system is evolved via damped Newtonian dynamics with additional shear and bending terms for mesh stability. The resulting surface demonstrates how the exponential spreading of geodesics in hyperbolic geometry manifests as physical buckling when the surface is embedded in flat space.
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