An implicit surface is the set of points $(x, y, z)$ satisfying \[ G(x,\, y,\, z,\, t) \;=\; 0 \] for a given scalar function $G$. To visualise such a surface, we sample $G$ on a regular voxel grid covering $[-L,\,L]^3$ and apply the marching cubes algorithm: each cubic cell whose eight corner values straddle zero is classified into one of 256 topological configurations via a lookup table. The precise zero-crossing on every active edge is found by bisection (six iterations, locating the root to $\sim\!1/64$ of the cell width). The resulting vertices are assembled into triangles and shaded using the analytic surface normal \[ \hat{\mathbf{n}} \;=\; \frac{\nabla G}{\lVert \nabla G \rVert}, \qquad \nabla G \;=\; \Bigl(\tfrac{\partial G}{\partial x},\; \tfrac{\partial G}{\partial y},\; \tfrac{\partial G}{\partial z}\Bigr) \] approximated by central finite differences.
Drag to orbit, scroll or use arrow keys to zoom. Try the different surfaces in the dropdown — some evolve in time while others are static but can be explored from any angle.