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77 lines
2.2 KiB
Python
77 lines
2.2 KiB
Python
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"""Authors Bastien Capiaux & Mehdi Oudghiri
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The Vicsek fractal algorithm is a recursive algorithm that creates a
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pattern known as the Vicsek fractal or the Vicsek square.
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It is based on the concept of self-similarity, where the pattern at each
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level of recursion resembles the overall pattern.
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The algorithm involves dividing a square into 9 equal smaller squares,
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removing the center square, and then repeating this process on the remaining 8 squares.
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This results in a pattern that exhibits self-similarity and has a
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square-shaped outline with smaller squares within it.
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Source: https://en.wikipedia.org/wiki/Vicsek_fractal
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"""
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import turtle
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def draw_cross(x: float, y: float, length: float):
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"""
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Draw a cross at the specified position and with the specified length.
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"""
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turtle.up()
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turtle.goto(x - length / 2, y - length / 6)
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turtle.down()
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turtle.seth(0)
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turtle.begin_fill()
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for _ in range(4):
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turtle.fd(length / 3)
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turtle.right(90)
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turtle.fd(length / 3)
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turtle.left(90)
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turtle.fd(length / 3)
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turtle.left(90)
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turtle.end_fill()
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def draw_fractal_recursive(x: float, y: float, length: float, depth: float):
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"""
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Recursively draw the Vicsek fractal at the specified position, with the
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specified length and depth.
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"""
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if depth == 0:
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draw_cross(x, y, length)
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return
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draw_fractal_recursive(x, y, length / 3, depth - 1)
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draw_fractal_recursive(x + length / 3, y, length / 3, depth - 1)
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draw_fractal_recursive(x - length / 3, y, length / 3, depth - 1)
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draw_fractal_recursive(x, y + length / 3, length / 3, depth - 1)
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draw_fractal_recursive(x, y - length / 3, length / 3, depth - 1)
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def set_color(rgb: str):
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turtle.color(rgb)
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def draw_vicsek_fractal(x: float, y: float, length: float, depth: float, color="blue"):
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"""
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Draw the Vicsek fractal at the specified position, with the specified
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length and depth.
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"""
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turtle.speed(0)
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turtle.hideturtle()
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set_color(color)
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draw_fractal_recursive(x, y, length, depth)
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turtle.Screen().update()
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def main():
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draw_vicsek_fractal(0, 0, 800, 4)
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turtle.done()
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if __name__ == "__main__":
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main()
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