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    Wow! I am very impressed with your work, as usual. Expect a bounty when the timer allows me to. If I may ask, why does the more dense tessellation seem to occur along one of the long diagonals, and not the other? Wouldn't you expect it to be more radially centred around the origin? Commented Oct 20 at 17:22
  • One problem I've noticed: Triangles which are adjacent to more subdivided ones can have gaps when the subdivided ones interpolate an interior point along a line segment. Commented Oct 20 at 18:20
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    Thanks for the kind words! The diagonal bias comes from the rectangular initial grid—it doesn’t perfectly capture the radial symmetry of the function. The gaps appear because refinement is non‑conforming: when one triangle is split but its neighbour isn’t, T‑junctions form. A fully conforming mesh (where every shared vertex belongs to all adjacent triangles) would fix this, but it requires maintaining mesh topology, which greatly complicates the code. I’m still thinking about these issues. It would be worth looking into how this is handled (or isn’t) in FEM. Commented Oct 21 at 4:36
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    +1. Sometimes I wonder if people will implement a computer algebra system entirely in Lua, LaTeX and TikZ!! Commented Oct 25 at 12:01
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    @ApoorvPotnis Thanks! Well, according to the Church–Turing thesis, if something is computable at all, it can be done in Lua—after all, Lua is Turing-complete. Whether it should be done in TikZ… that’s a question for the typesetting gods. 😅 Commented Oct 25 at 12:14