uk.ac.starlink.ttools.scheme

Class AttractorFamily

java.lang.Object

uk.ac.starlink.ttools.scheme.AttractorFamily

public abstract class AttractorFamily
extends Object

Defines an interface and some implementations for a family of (potentially) strange attractors.

Since:

21 Jul 2020

Author:

Mark Taylor

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	AttractorFamily.Attractor Defines an unbounded sequence of points, that may represent an attractor.

Field Summary

Fields

Modifier and Type	Field and Description
static AttractorFamily	CLIFFORD Clifford attractors; 2d, with four parameters.
static AttractorFamily	HENON Henon attractors; 2d, with three parameters (quite boring).
static AttractorFamily	RAMPE Rampe attractors; 3d, wit six parameters.

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	AttractorFamily(String name, int ndim, int nparam, double maxAbsParam, double fillThresh) Constructor.

Method Summary

Modifier and Type	Method and Description
AttractorFamily.Attractor	createAttractor(double[] params, double[] seed) Creates an attractor in this family by supplying numeric parameters.
AttractorFamily.Attractor	createAttractor(Random rnd) Creates a random attractor in this family.
abstract java.util.function.UnaryOperator<double[]>	createOperator(double[] params) Returns the operator which produces the next ndim-element output point from the previous one.
int	getDimCount() Returns the dimensionality of points in the sequence generated by attractors from this family.
abstract String	getDocUrl() Returns a URL on the WWW at which additional or background information about this attractor family may be found.
abstract String[]	getEquations() Returns a list of lines giving a textual representation of the iteration formula used to generate attractors.
abstract double[][]	getExamples() Returns a hard coded list of attractor parameter arrays that represent interesting members of this family.
double	getFillThreshold() Returns a guideline value for the space filling factor which represents an interesting (strange) attractor from this family.
double	getMaxAbsParam() The maximum absolute value recommended for each of the input values (which should therefore be in the range [-maxAbsParam,+maxAbsParam]).
String	getName() Returns the name of this family.
int	getParamCount() Returns the number of parameters required to produce an attractor instance.
static double	getSpaceFraction(AttractorFamily.Attractor att, int nbin) Calculates a measure of the proportion of the N-dimensional space defined by the bounds of an attractor.
static java.util.stream.Stream<AttractorFamily.Attractor>	getStrangeAttractors(AttractorFamily family) Utility/example method to create a stream of strange attractors in a given family.
static double[]	randoms(Random rnd, int n, double absmax) Returns a fixed size array containing random numbers suitable for use as attractor parameters.

Methods inherited from class java.lang.Object

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

Field Detail

CLIFFORD

public static final AttractorFamily CLIFFORD

Clifford attractors; 2d, with four parameters.

See Also:

https://examples.pyviz.org/attractors/attractors.html

RAMPE

public static final AttractorFamily RAMPE

Rampe attractors; 3d, wit six parameters.

See Also:

https://softologyblog.wordpress.com/2009/10/19/3d-strange-attractors/

HENON

public static final AttractorFamily HENON

Henon attractors; 2d, with three parameters (quite boring).

See Also:

https://en.wikipedia.org/wiki/H%C3%A9non_map

Constructor Detail

AttractorFamily

protected AttractorFamily(String name,
                          int ndim,
                          int nparam,
                          double maxAbsParam,
                          double fillThresh)

Constructor.

Parameters:

name - name of family

ndim - dimensionality of output points

nparam - number of numerical parameters required to define an attractor

maxAbsParam - the maximum absolute recommended value of each of the numerical parameters

fillThresh - guideline space filling factor above which attractors in this family look interesting (strange)

Method Detail

getName

public String getName()

Returns the name of this family.

Returns:

name

getDimCount

public int getDimCount()

Returns the dimensionality of points in the sequence generated by attractors from this family.

Returns:

output space dimensionality

getParamCount

public int getParamCount()

Returns the number of parameters required to produce an attractor instance.

Returns:

number of required numeric parameters

getMaxAbsParam

public double getMaxAbsParam()

The maximum absolute value recommended for each of the input values (which should therefore be in the range [-maxAbsParam,+maxAbsParam]).

Returns:

range for numeric parameters

getFillThreshold

public double getFillThreshold()

Returns a guideline value for the space filling factor which represents an interesting (strange) attractor from this family. Many or most attractors in a given family are quite boring (not strange).

Returns:

approximate space fraction threshold for strangeness

See Also:

getSpaceFraction(uk.ac.starlink.ttools.scheme.AttractorFamily.Attractor, int)

getEquations

public abstract String[] getEquations()

Returns a list of lines giving a textual representation of the iteration formula used to generate attractors. The expectation is that this will be displayed in a fixed-width font, with one element per display line.

Returns:

textual representation of iteration equations

getDocUrl

public abstract String getDocUrl()

Returns a URL on the WWW at which additional or background information about this attractor family may be found.

Returns:

documentation URL, or null if none known

createOperator

public abstract java.util.function.UnaryOperator<double[]> createOperator(double[] params)

Returns the operator which produces the next ndim-element output point from the previous one.

Parameters:

params - nparam-element list of numeric parameters defining the attractor

Returns:

point generator function

createAttractor

public AttractorFamily.Attractor createAttractor(double[] params,
                                                 double[] seed)

Creates an attractor in this family by supplying numeric parameters.

Parameters:

params - nparam-element array of numeric parameters

seed - initial point for iteration, or null for default

Returns:

attractor

createAttractor

public AttractorFamily.Attractor createAttractor(Random rnd)

Creates a random attractor in this family.

Parameters:

rnd - random seed

Returns:

attractor

getExamples

public abstract double[][] getExamples()

Returns a hard coded list of attractor parameter arrays that represent interesting members of this family. Suitable examples can be generated by running getStrangeAttractors(uk.ac.starlink.ttools.scheme.AttractorFamily). This list should contain at least one entry.

Returns:

example parameter arrays for strange attractors

randoms

public static double[] randoms(Random rnd,
                               int n,
                               double absmax)

Returns a fixed size array containing random numbers suitable for use as attractor parameters. The values are reasonably "round", which means they can be written down without a lot of significant figures.

Parameters:

rnd - random seed

n - required size of output array

absmax - absolute maximum value

Returns:

n-element array of values each in the range [-absmax,+absmax]

getSpaceFraction

public static double getSpaceFraction(AttractorFamily.Attractor att,
                                      int nbin)

Calculates a measure of the proportion of the N-dimensional space defined by the bounds of an attractor. This is a useful value for identifying "interesting" attractors; boring/non-strange ones may collapse down to a small number of points or lines, but ones which return a high value probably look nice.

Of course the actual proporition for a finite number of points is effectively zero, but we bin the space up into a regular grid and count how many of the grid elements are hit during iteration.

Parameters:

att - attractor to characterise

nbin - number of bins along each axis

Returns:

proportion of bins that are covered by a sequence of iterations

getStrangeAttractors

public static java.util.stream.Stream<AttractorFamily.Attractor> getStrangeAttractors(AttractorFamily family)

Utility/example method to create a stream of strange attractors in a given family.

Parameters:

family - attractor family

Returns:

stream of strange attractors