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Seven puzzles, one screen. This build arranges 2 x n x 1 Rubik’s-style puzzles (n=1,2,..,7) in a circle and performs a random walk of each of their state graphs in real time. As each move fires, the current puzzle changes state and its state space graph "grows" with nodes appear only when first visited, each with a mini-puzzle mirroring the exact configuration.

Built in C++17 with OpenGL with instanced rendering, batched edges, and spatial-hash physics for layouts with a tracer that rides the currently executed generator, placed over the associated mini-puzzle (a copy of the specific state that the puzzle is in at that place in statespace).

What you’ll see

7 simultaneous puzzles (1–7 layers) arranged in a circle

Real-time random walks on each puzzle’s state space

On-demand nodes: a graph node only spawns when visited

Color-coded edges for generators.

Mini-puzzles at each vertex that match the node’s state

C++17, OpenGL 3.3 core, GLFW, GLEW, GLM

Instanced spheres for nodes; single draw-call batched lines for edges

Force-directed physics with O(n) repulsion via spatial hashing

Group-theory flavour: states as nodes; edges as generators.

Engine stats: ~3k+ lines of C++ and a custom render pipeline

Notes

This video showcases sizes 1–7; size 8 is omitted due to memory blow-up during full enumeration on consumer hardware.

If you like math/CS visualizations - Rubik’s groups, permutation groups, graph layouts, or graphics programming - subscribe for bigger state spaces and deeper group relations.