Generative app · Technical writeup

Tensor Fractal Studio

A web application that treats a three-dimensional fractal as the projection of a tensor field. Each iterate applies a 3×3 tensor T, a scale vector s, and an offset vector b, then a nonlinear map: Mandelbulb power, quaternion Julia, Mandelbox fold, or a raw tensor-power field. The surface is sphere-traced from a distance estimator so the camera can zoom until the epsilon is smaller than a pixel.

Open the live studio

Generator

z ← T z ⊙ s + b, then z ← f(z, c, n). T ∈ R³ˣ³ is edited cell by cell. s and b are axis sliders. c is a quaternion seed for Julia and a translational seed for the tensor field. n is the spherical power. Lighting is two-light Blinn-Phong, orbit-trap albedo, five-tap ambient occlusion, Fresnel rim, exponential fog, and Reinhard tonemap.

Interaction

  • Drag on the canvas to orbit the camera (azimuth / elevation).
  • Use the mouse wheel to zoom in and out.
  • Switch between four formulas to transform the geometry.
  • Edit the tensor cells and sliders to reshape the surface in real time.
  • Apply built-in presets or save your own.