Class GingerbreadManMap

java.lang.Object

org.episteme.core.mathematics.analysis.chaos.GingerbreadManMap

All Implemented Interfaces:

Function<Real[],Real[]>, DiscreteMap<Real[]>, Function<Real[],Real[]>, Relation<Real[],Real[]>

public class GingerbreadManMap
extends Object
implements DiscreteMap<Real[]>

The Gingerbread Man Map - a chaotic discrete dynamical system.

Defined by the recurrence relations:

x(n+1) = 1 - y(n) + |x(n)|
y(n+1) = x(n)

This map produces a distinctive gingerbread-man-shaped fractal attractor.

Properties

• Strange attractor with fractal structure
• Basin of attraction includes most of the plane
• Exhibits sensitive dependence on initial conditions

References

• Devaney, R. L. (1989). "An Introduction to Chaotic Dynamical Systems"

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
GingerbreadManMap()

Method Summary

Modifier and Type	Method	Description
Real[]	evaluate(Real[] state)	Evaluates this function at the given point.
Real[][]	generateTrajectory(double x0, double y0, int iterations)	Generates a trajectory starting from initial conditions.
int	getDimension()
static double[]	plotBounds()	Suggested plot bounds for the attractor.
String	toString()
static double[]	typicalInitialConditions()	Typical initial conditions for visualization.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface DiscreteMap

getLyapunovExponent, iterate

Methods inherited from interface Function

compose

Methods inherited from interface Function

andThen, apply, compose, contains, evaluate, getBackend, isContinuous, isDifferentiable, setBackend

Methods inherited from interface Relation

getCodomain, getDomain

Constructor Details

GingerbreadManMap

public GingerbreadManMap()

Method Details

evaluate

public Real[] evaluate(Real[] state)

Description copied from interface: Function

Evaluates this function at the given point.

Specified by:

evaluate in interface Function<Real[],Real[]>

Parameters:

state - the input point

Returns:

the value of the function at x

getDimension

public int getDimension()

generateTrajectory

public Real[][] generateTrajectory(double x0,
 double y0,
 int iterations)

Generates a trajectory starting from initial conditions.

Parameters:

x0 - initial x coordinate

y0 - initial y coordinate

iterations - number of iterations

Returns:

array of points [x, y] forming the trajectory

typicalInitialConditions

public static double[] typicalInitialConditions()

Typical initial conditions for visualization.

Returns:

array [x0, y0]

plotBounds

public static double[] plotBounds()

Suggested plot bounds for the attractor.

Returns:

array [xMin, xMax, yMin, yMax]

toString

public String toString()

Overrides:

toString in class Object