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Rose Sinusoids and 2D Rotations

Rose sinusoids or rhodonea curves are polar coordinate curves.

Attribution

Rose sinusoids
September 2026
Image: NMoroney

Wikipedia has a nice reference chart for different variations.

I wrote a C++ version that I had Gemini port to Python :

fleuron

The initial version used Eigen to 2D rotate the sinusoid.

For the Gemini session exit summary, the report was processed with this code.

Interaction Summary
  Tool Calls:                 5 ( ✓ 5 x 0 )
  Success Rate:               100.0%
  User Agreement:             100.0% (5 reviewed)
  Code Changes:               +80 -0

  Performance
  Wall Time:                  59.9s
  Agent Active:               25.7s
    » API Time:               16.0s (62.2%)
    » Tool Time:              9.7s (37.8%)


  Model Usage
  Use /model to view model quota information

  Model                           Reqs  Input Tokens   Cache Reads Output Token
  ─────────────────────────────────────────────────────────────────────────────
  gemini-3.1-flash-lite              1           755             0            1
    ↳ utility_summarizer             1           755             0            1
  gemini-3-flash-preview             4        47,632        11,232         1,29
    ↳ main                           4        47,632        11,232         1,29
╰──────────────────────────────────────────────────────────────────────────────

Which makes me wonder, what else can 50K tokens get you?


2026-09-09
NMoroney