Class MandelbrotSet

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

The Mandelbrot set M ⊂ ℂ is defined as: M = { c ∈ ℂ : the sequence z₀ = 0, zₙ₊₁ = zₙ² + c remains bounded }

References

  • Benoit B. Mandelbrot, "The Fractal Geometry of Nature", W.H. Freeman and Company, 1982
  • Adrien Douady and John H. Hubbard, "Étude dynamique des polynômes complexes", Publications Mathématiques d'Orsay, 1984-1985
Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Details

    • MandelbrotSet

      public MandelbrotSet()

    • MandelbrotSet

      public MandelbrotSet(int maxIterations)

  • Method Details

    • contains

      public boolean contains(Complex c)
      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:
      c - 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 c)

    • getMaxIterations

      public int getMaxIterations()