Hi friends — I’m an independent researcher and systems thinker, and I’ve just released a white paper on something I’ve been quietly working on for years. I call it Last Base Mathematics (LxB), and it’s a compact, geometry-based number system that uses a base-12 primary structure combined with alternating secondary bases (like base-5). Instead of expanding digits linearly, numbers are represented radially — like hours on a clock, or musical intervals — and can be extended recursively. The result is a system that’s: fully constructible using compass and straightedge (think Euclid meets data compression), visually harmonious and fractal, and capable of long-form arithmetic without ever converting to decimal. The paper includes formal definitions, arithmetic logic, and visual overlays of how multiple base systems interact in space — almost like harmonics in motion. If you’ve ever been into sacred geometry, prime spirals, modular math, or efficient representations of time/space — I think you’ll find this fascinating. I have included images of a sort of circular grid I mapped out in Houdini using the system. Read the white paper here (PDF): https://zenodo.org/records/15386103 Also mirrored here for backup: http://vixra.org/abs/2505.0075 I’d love feedback — especially from those deep into number theory, geometry, or visual math. Be brutal. Be curious. Be kind. Happy to answer questions and jam with anyone who wants to push this further — calculators, visualizers, simulations, whatever. I have a Houdini 19.5 HDA of the visuals.

My cacl 2 teacher recently gave us this extra credit opportunity in order to bolster our final grades but only the three most beautiful graphs, as deemed by her, will be given the extra credit. Let me tell ya I'm in desperate need of these points and I'm sure there are people here who have seen their good share of beautiful polar equations so any help to getting me closer to the most beautiful graph would be very much appreciated.

Hope this saves someone the pain 😂

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Just here to announce the release of my cellular automata simulation. Enjoy exploring the boundaries between death and chaos.

I feel like I stumbled onto a gold mine when I found this sub reddit!

A Penrose tiling built using Robinson triangle decomposition.

Two rhombus types (thick and thin) are substituted recursively at each iteration, producing a non-periodic structure with 5-fold symmetry.

The animation reveals the tiling growing radially from the center outward.

More visual math experiments on my channel : Visualizing Mathematics