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87 lines
2.7 KiB
Python
87 lines
2.7 KiB
Python
"""
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Author Anurag Kumar | anuragkumarak95@gmail.com | git/anuragkumarak95
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Simple example of fractal generation using recursion.
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What is the Sierpiński Triangle?
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The Sierpiński triangle (sometimes spelled Sierpinski), also called the
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Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with
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the overall shape of an equilateral triangle, subdivided recursively into
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smaller equilateral triangles. Originally constructed as a curve, this is one of
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the basic examples of self-similar sets—that is, it is a mathematically
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generated pattern that is reproducible at any magnification or reduction. It is
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named after the Polish mathematician Wacław Sierpiński, but appeared as a
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decorative pattern many centuries before the work of Sierpiński.
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Usage: python sierpinski_triangle.py <int:depth_for_fractal>
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Credits:
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The above description is taken from
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https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle
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This code was written by editing the code from
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https://www.riannetrujillo.com/blog/python-fractal/
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"""
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import sys
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import turtle
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def get_mid(p1: tuple[float, float], p2: tuple[float, float]) -> tuple[float, float]:
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"""
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Find the midpoint of two points
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>>> get_mid((0, 0), (2, 2))
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(1.0, 1.0)
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>>> get_mid((-3, -3), (3, 3))
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(0.0, 0.0)
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>>> get_mid((1, 0), (3, 2))
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(2.0, 1.0)
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>>> get_mid((0, 0), (1, 1))
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(0.5, 0.5)
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>>> get_mid((0, 0), (0, 0))
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(0.0, 0.0)
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"""
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return (p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2
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def triangle(
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vertex1: tuple[float, float],
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vertex2: tuple[float, float],
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vertex3: tuple[float, float],
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depth: int,
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) -> None:
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"""
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Recursively draw the Sierpinski triangle given the vertices of the triangle
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and the recursion depth
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"""
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my_pen.up()
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my_pen.goto(vertex1[0], vertex1[1])
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my_pen.down()
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my_pen.goto(vertex2[0], vertex2[1])
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my_pen.goto(vertex3[0], vertex3[1])
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my_pen.goto(vertex1[0], vertex1[1])
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if depth == 0:
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return
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triangle(vertex1, get_mid(vertex1, vertex2), get_mid(vertex1, vertex3), depth - 1)
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triangle(vertex2, get_mid(vertex1, vertex2), get_mid(vertex2, vertex3), depth - 1)
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triangle(vertex3, get_mid(vertex3, vertex2), get_mid(vertex1, vertex3), depth - 1)
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if __name__ == "__main__":
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if len(sys.argv) != 2:
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raise ValueError(
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"Correct format for using this script: "
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"python fractals.py <int:depth_for_fractal>"
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)
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my_pen = turtle.Turtle()
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my_pen.ht()
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my_pen.speed(5)
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my_pen.pencolor("red")
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vertices = [(-175, -125), (0, 175), (175, -125)] # vertices of triangle
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triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))
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turtle.Screen().exitonclick()
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