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Geometric Construction of the 4^4 Regular Tiling

Geometric Construction of the 4^4 Regular Tiling
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2025-01-27 21:41
In collections La fábrica de teselados
This example demonstrates how a “4^4” regular tiling pattern is generated and iteratively extended on the plane, producing the characteristic symmetric tessellation layout. The core mathematical ideas include regular tilings (encoded by vertex configuration), geometric relationships involving circles and polygons, and construction via symmetry/translation transforms. From the construction summary,

GeoGebra Commands & Parameters

  1. Translate(lista1, t) → tras1
  2. Translate(lista2, t) → tras2
  3. Circle((0, 0), 4) → c
  4. Mirror(tras1, c) → inv1
  5. Mirror(tras2, c) → inv2
  6. Corner(1, 1) → Export_1
  7. Corner(1, 3) → Export_2
  8. Translate(lista3, t) → tras3
  9. Mirror(tras3, c) → inv3
  10. Translate(lista4, t) → tras4
  11. Mirror(tras4, c) → inv4
  12. Sequence({random(), random(), random()}, k, 1, númeroListas) → listaAzar
  13. Sequence(If[oscuro, {1, 1, 1}, {0, 0, 0}], k, 1, númeroListas) → listaBorde