Class KochCurve

java.lang.Object

org.episteme.core.mathematics.analysis.chaos.KochCurve

public class KochCurve
extends Object

Koch Curve (Snowflake) - a fractal curve.

The Koch curve is constructed by recursive subdivision:

1. Start with a line segment
2. Divide it into thirds
3. Replace the middle third with two sides of an equilateral triangle
4. Repeat for each segment

Properties

• Hausdorff dimension: log(4)/log(3) ≈ 1.2619
• Infinite length in finite area
• Continuous but nowhere differentiable
• Self-similar at all scales

References

• von Koch, Helge (1904). "Sur une courbe continue sans tangente"
• Mandelbrot, B. (1982). "The Fractal Geometry of Nature"

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
KochCurve()

Method Summary

Modifier and Type	Method	Description
static double	curveLength(double initialLength, int depth)	Calculates the length of the Koch curve at a given depth.
static List<Point2D>	generate(Point2D start, Point2D end, int depth)	Generates the Koch curve up to a given depth.
static List<Point2D>	generateSnowflake(Point2D center, double radius, int depth)	Generates a Koch snowflake (3 Koch curves forming a triangle).
static double	hausdorffDimension()	Calculates the Hausdorff dimension of the Koch curve.

Methods inherited from class Object

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

Constructor Details

KochCurve

public KochCurve()

Method Details

generate

public static List<Point2D> generate(Point2D start,
 Point2D end,
 int depth)

Generates the Koch curve up to a given depth.

Parameters:

start - starting point

end - ending point

depth - recursion depth (0 = line segment)

Returns:

list of points forming the curve

generateSnowflake

public static List<Point2D> generateSnowflake(Point2D center,
 double radius,
 int depth)

Generates a Koch snowflake (3 Koch curves forming a triangle).

Parameters:

center - center of the snowflake

radius - radius of the enclosing circle

depth - recursion depth

Returns:

list of points forming the snowflake

hausdorffDimension

public static double hausdorffDimension()

Calculates the Hausdorff dimension of the Koch curve.

Returns:

log(4)/log(3) ≈ 1.2619

curveLength

public static double curveLength(double initialLength,
 int depth)

Calculates the length of the Koch curve at a given depth.

Parameters:

initialLength - length of the initial segment

depth - recursion depth

Returns:

total length