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Maxim Smolskiy
2024-03-28 21:03:23 +03:00
committed by GitHub
parent efb7463cde
commit f2246ce7fd
8 changed files with 121 additions and 128 deletions
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54
fractals/julia_sets.py
View File

@ -25,8 +25,8 @@ import warnings
from collections.abc import Callable
from typing import Any
import numpy
from matplotlib import pyplot
import matplotlib.pyplot as plt
import numpy as np
c_cauliflower = 0.25 + 0.0j
c_polynomial_1 = -0.4 + 0.6j
@ -37,22 +37,20 @@ window_size = 2.0
nb_pixels = 666
def eval_exponential(c_parameter: complex, z_values: numpy.ndarray) -> numpy.ndarray:
def eval_exponential(c_parameter: complex, z_values: np.ndarray) -> np.ndarray:
"""
Evaluate $e^z + c$.
>>> eval_exponential(0, 0)
1.0
>>> abs(eval_exponential(1, numpy.pi*1.j)) < 1e-15
>>> abs(eval_exponential(1, np.pi*1.j)) < 1e-15
True
>>> abs(eval_exponential(1.j, 0)-1-1.j) < 1e-15
True
"""
return numpy.exp(z_values) + c_parameter
return np.exp(z_values) + c_parameter
def eval_quadratic_polynomial(
c_parameter: complex, z_values: numpy.ndarray
) -> numpy.ndarray:
def eval_quadratic_polynomial(c_parameter: complex, z_values: np.ndarray) -> np.ndarray:
"""
>>> eval_quadratic_polynomial(0, 2)
4
@ -66,7 +64,7 @@ def eval_quadratic_polynomial(
return z_values * z_values + c_parameter
def prepare_grid(window_size: float, nb_pixels: int) -> numpy.ndarray:
def prepare_grid(window_size: float, nb_pixels: int) -> np.ndarray:
"""
Create a grid of complex values of size nb_pixels*nb_pixels with real and
imaginary parts ranging from -window_size to window_size (inclusive).
@ -77,20 +75,20 @@ def prepare_grid(window_size: float, nb_pixels: int) -> numpy.ndarray:
[ 0.-1.j, 0.+0.j, 0.+1.j],
[ 1.-1.j, 1.+0.j, 1.+1.j]])
"""
x = numpy.linspace(-window_size, window_size, nb_pixels)
x = np.linspace(-window_size, window_size, nb_pixels)
x = x.reshape((nb_pixels, 1))
y = numpy.linspace(-window_size, window_size, nb_pixels)
y = np.linspace(-window_size, window_size, nb_pixels)
y = y.reshape((1, nb_pixels))
return x + 1.0j * y
def iterate_function(
eval_function: Callable[[Any, numpy.ndarray], numpy.ndarray],
eval_function: Callable[[Any, np.ndarray], np.ndarray],
function_params: Any,
nb_iterations: int,
z_0: numpy.ndarray,
z_0: np.ndarray,
infinity: float | None = None,
) -> numpy.ndarray:
) -> np.ndarray:
"""
Iterate the function "eval_function" exactly nb_iterations times.
The first argument of the function is a parameter which is contained in
@ -98,22 +96,22 @@ def iterate_function(
values to iterate from.
This function returns the final iterates.
>>> iterate_function(eval_quadratic_polynomial, 0, 3, numpy.array([0,1,2])).shape
>>> iterate_function(eval_quadratic_polynomial, 0, 3, np.array([0,1,2])).shape
(3,)
>>> numpy.round(iterate_function(eval_quadratic_polynomial,
>>> np.round(iterate_function(eval_quadratic_polynomial,
... 0,
... 3,
... numpy.array([0,1,2]))[0])
... np.array([0,1,2]))[0])
0j
>>> numpy.round(iterate_function(eval_quadratic_polynomial,
>>> np.round(iterate_function(eval_quadratic_polynomial,
... 0,
... 3,
... numpy.array([0,1,2]))[1])
... np.array([0,1,2]))[1])
(1+0j)
>>> numpy.round(iterate_function(eval_quadratic_polynomial,
>>> np.round(iterate_function(eval_quadratic_polynomial,
... 0,
... 3,
... numpy.array([0,1,2]))[2])
... np.array([0,1,2]))[2])
(256+0j)
"""
@ -121,8 +119,8 @@ def iterate_function(
for _ in range(nb_iterations):
z_n = eval_function(function_params, z_n)
if infinity is not None:
numpy.nan_to_num(z_n, copy=False, nan=infinity)
z_n[abs(z_n) == numpy.inf] = infinity
np.nan_to_num(z_n, copy=False, nan=infinity)
z_n[abs(z_n) == np.inf] = infinity
return z_n
@ -130,21 +128,21 @@ def show_results(
function_label: str,
function_params: Any,
escape_radius: float,
z_final: numpy.ndarray,
z_final: np.ndarray,
) -> None:
"""
Plots of whether the absolute value of z_final is greater than
the value of escape_radius. Adds the function_label and function_params to
the title.
>>> show_results('80', 0, 1, numpy.array([[0,1,.5],[.4,2,1.1],[.2,1,1.3]]))
>>> show_results('80', 0, 1, np.array([[0,1,.5],[.4,2,1.1],[.2,1,1.3]]))
"""
abs_z_final = (abs(z_final)).transpose()
abs_z_final[:, :] = abs_z_final[::-1, :]
pyplot.matshow(abs_z_final < escape_radius)
pyplot.title(f"Julia set of ${function_label}$, $c={function_params}$")
pyplot.show()
plt.matshow(abs_z_final < escape_radius)
plt.title(f"Julia set of ${function_label}$, $c={function_params}$")
plt.show()
def ignore_overflow_warnings() -> None:

34
fractals/koch_snowflake.py
View File

@ -22,25 +22,25 @@ Requirements (pip):
from __future__ import annotations
import matplotlib.pyplot as plt # type: ignore
import numpy
import matplotlib.pyplot as plt
import numpy as np
# initial triangle of Koch snowflake
VECTOR_1 = numpy.array([0, 0])
VECTOR_2 = numpy.array([0.5, 0.8660254])
VECTOR_3 = numpy.array([1, 0])
VECTOR_1 = np.array([0, 0])
VECTOR_2 = np.array([0.5, 0.8660254])
VECTOR_3 = np.array([1, 0])
INITIAL_VECTORS = [VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]
# uncomment for simple Koch curve instead of Koch snowflake
# INITIAL_VECTORS = [VECTOR_1, VECTOR_3]
def iterate(initial_vectors: list[numpy.ndarray], steps: int) -> list[numpy.ndarray]:
def iterate(initial_vectors: list[np.ndarray], steps: int) -> list[np.ndarray]:
"""
Go through the number of iterations determined by the argument "steps".
Be careful with high values (above 5) since the time to calculate increases
exponentially.
>>> iterate([numpy.array([0, 0]), numpy.array([1, 0])], 1)
>>> iterate([np.array([0, 0]), np.array([1, 0])], 1)
[array([0, 0]), array([0.33333333, 0. ]), array([0.5 , \
0.28867513]), array([0.66666667, 0. ]), array([1, 0])]
"""
@ -50,13 +50,13 @@ def iterate(initial_vectors: list[numpy.ndarray], steps: int) -> list[numpy.ndar
return vectors
def iteration_step(vectors: list[numpy.ndarray]) -> list[numpy.ndarray]:
def iteration_step(vectors: list[np.ndarray]) -> list[np.ndarray]:
"""
Loops through each pair of adjacent vectors. Each line between two adjacent
vectors is divided into 4 segments by adding 3 additional vectors in-between
the original two vectors. The vector in the middle is constructed through a
60 degree rotation so it is bent outwards.
>>> iteration_step([numpy.array([0, 0]), numpy.array([1, 0])])
>>> iteration_step([np.array([0, 0]), np.array([1, 0])])
[array([0, 0]), array([0.33333333, 0. ]), array([0.5 , \
0.28867513]), array([0.66666667, 0. ]), array([1, 0])]
"""
@ -74,22 +74,22 @@ def iteration_step(vectors: list[numpy.ndarray]) -> list[numpy.ndarray]:
return new_vectors
def rotate(vector: numpy.ndarray, angle_in_degrees: float) -> numpy.ndarray:
def rotate(vector: np.ndarray, angle_in_degrees: float) -> np.ndarray:
"""
Standard rotation of a 2D vector with a rotation matrix
(see https://en.wikipedia.org/wiki/Rotation_matrix )
>>> rotate(numpy.array([1, 0]), 60)
>>> rotate(np.array([1, 0]), 60)
array([0.5 , 0.8660254])
>>> rotate(numpy.array([1, 0]), 90)
>>> rotate(np.array([1, 0]), 90)
array([6.123234e-17, 1.000000e+00])
"""
theta = numpy.radians(angle_in_degrees)
c, s = numpy.cos(theta), numpy.sin(theta)
rotation_matrix = numpy.array(((c, -s), (s, c)))
return numpy.dot(rotation_matrix, vector)
theta = np.radians(angle_in_degrees)
c, s = np.cos(theta), np.sin(theta)
rotation_matrix = np.array(((c, -s), (s, c)))
return np.dot(rotation_matrix, vector)
def plot(vectors: list[numpy.ndarray]) -> None:
def plot(vectors: list[np.ndarray]) -> None:
"""
Utility function to plot the vectors using matplotlib.pyplot
No doctest was implemented since this function does not have a return value