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Ulam Spiral Sequence Visualization with Transformation Animation

Ulam Spiral Sequence Visualization with Transformation Animation
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2025-02-05 18:36
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This example demonstrates the Ulam spiral visualization - a mathematical pattern where natural numbers are arranged in a spiral grid, revealing intriguing distribution patterns of prime numbers. Core mathematical concepts include: spiral number sequences, prime number distribution, coordinate transformations, geometric reflections and translations. Built using GeoGebra commands including Translate

GeoGebra Commands & Parameters

  1. Translate(lista1, t) → tras1
  2. Translate(lista2, t) → tras2
  3. Circle((0, 0), 5) → 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