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#!/usr/bin/env python3 | |
# -*- coding: utf-8 -*- | |
######################################################################################################################## | |
# The MIT License (MIT) | |
# | |
# Copyright (c) 2016 Andrés Correa Casablanca | |
# | |
# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated | |
# documentation files (the "Software"), to deal in the Software without restriction, including without limitation the | |
# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit | |
# persons to whom the Software is furnished to do so, subject to the following conditions: | |
# | |
# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the | |
# Software. | |
# | |
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE | |
# WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR | |
# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR | |
# OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. | |
######################################################################################################################## | |
from math import sin, cos, radians | |
from typing import Sequence, List, Tuple | |
from random import randint, seed | |
import colorsys | |
import numpy | |
import svgwrite | |
from time import time | |
deg60 = radians(60) | |
cos60, sin60 = cos(deg60), sin(deg60) | |
cos60n, sin60n = cos(-deg60), sin(-deg60) | |
rot60 = numpy.array([[cos60, -sin60], [sin60, cos60]]) | |
rot60n = numpy.array([[cos60n, -sin60n], [sin60n, cos60n]]) | |
def generate_chain(level=0, base_chain=['a']): | |
if 0 == level: | |
return base_chain | |
new_chain = [] | |
for rule in base_chain: | |
if rule in ['-', '+']: | |
new_chain.append(rule) | |
elif 'a' == rule: | |
new_chain += ['a', '-', 'b', '-', '-', 'b', '+', 'a', '+', '+', 'a', 'a', '+', 'b', '-'] | |
elif 'b' == rule: | |
new_chain += ['+', 'a', '-', 'b', 'b', '-', '-', 'b', '-', 'a', '+', '+', 'a', '+', 'b'] | |
return generate_chain(level - 1, new_chain) | |
def sum_2d_vectors(a: Tuple[float, float], b: Tuple[float, float]) -> Tuple[float, float]: | |
return a[0]+b[0], a[1]+b[1] | |
def infer_points_from_chain( | |
chain: Sequence[str], first_point: Tuple[float, float], segment_size: float | |
) -> List[Tuple[float, float]]: | |
to_right = (segment_size, 0) | |
to_left = (-segment_size, 0) | |
to_north_east = tuple(rot60.dot(numpy.array(to_right))) | |
to_south_east = tuple(rot60n.dot(numpy.array(to_right))) | |
to_north_west = tuple(rot60n.dot(numpy.array(to_left))) | |
to_south_west = tuple(rot60.dot(numpy.array(to_left))) | |
vectors_circle = [to_right, to_north_east, to_north_west, to_left, to_south_west, to_south_east] | |
vectors_index = 0 | |
current_point = first_point | |
points = [first_point] | |
for step in chain: | |
if step in ['a', 'b']: | |
current_point = sum_2d_vectors(current_point, vectors_circle[vectors_index]) | |
points.append(current_point) | |
elif '+' == step: | |
vectors_index = (vectors_index + 1) % 6 | |
elif '-' == step: | |
vectors_index = (vectors_index - 1) % 6 | |
return points | |
def compute_gosper_curve_by_rules(level=4): | |
return infer_points_from_chain( | |
generate_chain(level), | |
(2560.0, 3712.0), | |
3072.0 / 7.0**(level*0.5) | |
) | |
def main(): | |
gosper_points = compute_gosper_curve_by_rules(4) | |
svg_document = svgwrite.Drawing(filename="gosperCurve4.svg", size=("4096px", "4096px")) | |
n_points = len(gosper_points) | |
seed(time()) | |
hue_index = randint(0, 63) | |
for i in range(1, n_points): | |
rgb = colorsys.hls_to_rgb(hue_index/64.0, 0.75, 0.75) | |
hue_index = (hue_index + randint(0, 1)*2 - 1) % 64 | |
svg_document.add( | |
svg_document.line( | |
start=gosper_points[i-1], | |
end=gosper_points[i], | |
stroke=svgwrite.rgb(rgb[0]*255, rgb[1]*255, rgb[2]*255), | |
stroke_width=10, | |
stroke_linecap='round', | |
fill_opacity=0 | |
) | |
) | |
svg_document.save() | |
if __name__ == "__main__": | |
main() | |
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