fractals.hilbert_curve

Author Atharva Date | atharvad931@gmail.com | git/Atharva9621

The Hilbert Curve (also known as the Hilbert Space Filling Curve) is a continuous fractal space-filling curve and is a variant of the space-filling Peano curves.

Because it is space-filling, its Hausdorff dimension is 2. Precisely, its image is the unit square, whose dimension is 2 in any definition of dimension. Its graph is a compact set homeomorphic to the closed unit interval, with Hausdorff dimension 1.

Credits:

description adapted from https://en.wikipedia.org/wiki/Hilbert_curve

also see https://youtu.be/3s7h2MHQtxc?si=_qIusAJFHYfXIOKn

(3b1b - Hilbert’s Curve: Is infinite math useful?)

https://dl.acm.org/doi/pdf/10.1145/290200.290219

Requirements (pip):

• matplotlib

Functions

hilbert_curve(→ list[tuple[float, float]])	Params:
plot_hilbert_curve(→ None)	Plots the hilbert curve using mtplotlib
rotate_pnts(→ list[tuple[float, float]])	Rotates a list of points by a given angle (in multiples of 90 degrees).

Module Contents

fractals.hilbert_curve.hilbert_curve(center: tuple[float, float], level: int, side: float = 1, angle: int = 90) → list[tuple[float, float]]

Params:

center: Tuple[float, float]- The (x, y) center coordinate of the subsection. level: int- The recursion depth or subdivision level of the Hilbert curve. side : float, optional

The length of the side of the square region in which the curve is drawn.

angleint, optional

The initial rotation angle of the curve in degrees. It should be a multiple of 90 degrees. (default=90)

Returns:

pts: List[Tuple[float, float]] -

A list of points (x, y) representing the Hilbert curve for the given level.

Example:

>>> hilbert_curve((0, 0), 1, angle=0)
[(0.25, 0.25), (-0.25, 0.25), (-0.25, -0.25), (0.25, -0.25)]

fractals.hilbert_curve.plot_hilbert_curve(points: list[tuple[float, float]]) → None

Plots the hilbert curve using mtplotlib

Example

>>> plot_hilbert_curve([(-0.25, 0.25), (-0.25, -0.25), (0.25, -0.25), (0.25, 0.25)])

fractals.hilbert_curve.rotate_pnts(pnts: list[tuple[float, float]], angle: int) → list[tuple[float, float]]

Rotates a list of points by a given angle (in multiples of 90 degrees).

Since the rotation is limited to multiples of 90 degrees (90, 180, 270, 360), this function simply reorders the list of points accordingly. The rotation in each quadrant is achieved by adjusting the starting index of the list and wrapping around.

Parameters:

pntsList[Tuple[float, float]]

A list of tuples, where each tuple represents a point (x, y).

angleint

The angle of rotation, should be a multiple of 90 degrees (e.g., 90, 180, 270, 360).

Returns:

List[Tuple[float, float]]

A reordered list of points, rotated by the specified angle.

Example:

>>> rotate_pnts([(1, 1), (0, 1), (0, 0), (1, 0)], 90)
[(0, 1), (0, 0), (1, 0), (1, 1)]