Formal evolution and the fourth dimension.

Bloom manipulates 2-manifolds within four-dimensional space by deforming a two-dimensional triangulated mesh in four dimensions. This deformation is controlled by harmonically related sinusoidal functions that modulate vertex coordinates along each axis of 4-space (x, y, z, w). The result is an undulating 2-manifold with coordinates for each dimension. A stereographic projection of this 4D object into 3D enables high-quality, raytraced renderings. Shifting the sinusoidal phase along the fourth dimension (w) induces significant morphological changes in the 3D projection, with the cyclic nature of this process allowing for seamless looping of the evolving form. Composite structures emerge by superimposing multiple manifolds, each with different phase shift rates.