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Truchet Labyrinth Diagonals Construction (Part One)

Truchet Labyrinth Diagonals Construction (Part One)
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2020-03-11 16:56
PolygonSequenceIntegral
This example demonstrates the dynamic construction of a Truchet labyrinth pattern using diagonal sequences. Core math concepts include geometric constructions, sequences, polygon formation, integral calculus, and logarithmic functions. Key GeoGebra commands used are Sequence, Polygon, Midpoint, Semicircle, Segment, and motif4. Suitable for high school and above, exploring geometric distribution and parametric animations.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Random[0, 3], k, 1, (2 * n)], j, 1, (2 * n)) → Alea
  2. Polygon(G, H, 4) → poly5, e, f, g, h, I, J
  3. Midpoint(G, I) → K
  4. Midpoint(g) → L
  5. Semicircle(G, H) → k
  6. Segment(L, K) → i
  7. motif4(U, V) → liste4
  8. Sequence(Sequence[Rotate[motif4[(k, j), (k + 1, j)], ((Element[Alea, k, j] * 90))°, (k + 1 / 2, j + 1 / 2)], k, 1, (2 * n)], j, 1, n) → liste1
  9. Polygon(N, M, F, E) → poly1, n_1, m_1, f_1, e_1
  10. Polygon(U, V, 4) → poly2, a, b, c, d, A, B
  11. Sequence(E + (i, 0), i, 1, (2 * n)) → liste2
  12. Sequence(Segment[Element[liste2, i], Element[liste2, i] + (0, n)], i, 1, Length[liste2]) → liste3
  13. Sequence(E + (0, i), i, 1, n) → liste5
  14. Sequence(Segment[Element[liste5, i], Element[liste5, i] + ((2 * n), 0)], i, 1, Length[liste5]) → liste6