1 思路
绘制一个三角形，取三角形的三边中点，以每两个中点及其所在边共有的顶点，三个一组，组合成三个小三角形，对三个三角形进行绘制，如下图所示，分别为ADF，DBE，FEC，以上步骤再重复
2 Python程序
import turtle
t = turtle.Turtle()
t.hideturtle()
FillColors=[
'#CAE1FF',
'#FFEFDB',
'#8470FF',
'#FF6347',
'#FFDEAD',
'#C1FFC1'
]
def get_midpoint(a, b):
ax, ay = a
bx, by = b
return (ax bx) / 2, (ay by) / 2
def draw_triangle(a, b, c, depth):
ax, ay = a
bx, by = b
cx, cy = c
t.penup()
_tcolor = FillColors[depth % len(FillColors)]
t.color("black", _tcolor)
t.goto(ax, ay)
t.pendown()
t.begin_fill()
t.goto(bx, by)
t.goto(cx, cy)
t.goto(ax, ay)
t.end_fill()
t.penup()
def draw_sierpinski(triangle, depth):
a, b, c = triangle
draw_triangle(a, b, c, depth)
if depth == 0:
return
else:
d = get_midpoint(a, b)
e = get_midpoint(b, c)
f = get_midpoint(c, a)
draw_sierpinski([a, d, f], depth-1)
draw_sierpinski([d, b, e], depth-1)
draw_sierpinski([f, e, c], depth-1)
if __name__ == '__main__':
triangle = [[-200, -100], [0, 200], [200, -100]]
draw_sierpinski(triangle, 5)
turtle.done()
3 效果
