Fractal Realms of the Multiverse

These images display the Generalized Mandelbrot Sets for the function z → z^d + c. The different values of d create distinct mathematical landscapes, revealing alien-like mathematical structures in complex space.

Lyapunov exponent heatmaps display the chaotic regions of fractals generated by z → z^d + c. Darker regions indicate stable zones, while lighter ones highlight instability—chaotic voids in the fractal cosmos.

Julia sets depict the structure of individual orbit dynamics for specific values of c. These intricate designs resemble cosmic nebulae formed through complex iteration rules.

A Julia set visualization for z → 1/z² + c, presenting an inverted universe where fractal filaments emerge in counterintuitive symmetries.

The Mandelbrot-type set for z → 1/z² + c. Here, traditional fractal boundaries dissolve into novel bifurcation structures, exposing a strange mathematical cosmos.

Lyapunov exponent heatmap of an alternative Mandelbrot-type set. The interwoven layers of stability and chaos create a tapestry of multidimensional dynamics.

A Julia set for f(z) = 1/z² + c, highlighting its complex and often counterintuitive formations, resembling networks of interstellar filaments.

An alternate Mandelbrot set with unusual symmetry, revealing unique pathways of fractal exploration.

Lyapunov exponent heatmap showing the stability and chaotic behavior of a specialized Julia set, where chaos and order intertwine in a cosmic ballet.