Class JuliaSet

java.lang.Object
org.episteme.core.mathematics.analysis.chaos.JuliaSet
All Implemented Interfaces:
Set<Complex>
public class JuliaSet extends Object implements Set<Complex>
Julia Set as a proper mathematical set.

For a given complex parameter c, the Julia set J_c ⊂ ℂ is defined as: J_c = { z ∈ ℂ : the sequence z₀ = z, zₙ₊₁ = zₙ² + c remains bounded }

References

  • Gaston Julia, "Mémoire sur l'itération des fonctions rationnelles", Journal de Mathématiques Pures et Appliquées, Vol. 8, 1918, pp. 47-245
  • Benoit B. Mandelbrot, "The Fractal Geometry of Nature", W.H. Freeman and Company, 1982 (popularized Julia sets)
Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Details

    • JuliaSet

      public JuliaSet(Complex c)

    • JuliaSet

      public JuliaSet(Complex c, int maxIterations)

  • Method Details

    • contains

      public boolean contains(Complex z)
      Description copied from interface: Set
      Tests whether this set contains the specified element.

      This is the fundamental operation of a set - membership testing.

      Specified by:
      contains in interface Set<Complex>
      Parameters:
      z - the element to test for membership
      Returns:
      true if this set contains the element, false otherwise
      See Also:

    • isEmpty

      public boolean isEmpty()
      Description copied from interface: Set
      Returns true if this set contains no elements.

      The empty set (∅) is a fundamental concept in set theory. It is the unique set containing no elements.

      Specified by:
      isEmpty in interface Set<Complex>
      Returns:
      true if this set is empty

    • description

      public String description()
      Description copied from interface: Set
      Returns a human-readable description of this set.

      Examples:

      • "ℝ (Real Numbers)"
      • "ℤ/12ℤ (Integers modulo 12)"
      • "{1, 2, 3, 4, 5}"

      Specified by:
      description in interface Set<Complex>
      Returns:
      a description of this set

    • escapeTime

      public int escapeTime(Complex z)

    • getParameter

      public Complex getParameter()

    • getMaxIterations

      public int getMaxIterations()