In “Fractangular Frolics” I looked at how you could create fractals by choosing lines from a dissected equilateral or isosceles right triangle. Now I want to look at fractals created from the lines of a dissected diamond, as here:

Lines in a dissected diamond

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Let’s start by creating one of the most famous fractals of all, the Sierpiński triangle:

Sierpiński triangle stage 1

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Sierpiński triangle #2

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Sierpiński triangle #3

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Sierpiński triangle #4

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Sierpiński triangle #5

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Sierpiński triangle #6

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Sierpiński triangle #7

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Sierpiński triangle #8

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Sierpiński triangle #9

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Sierpiński triangle #10

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Sierpiński triangle (animated)

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However, you can get an infinite number of Sierpiński triangles with three lines from the diamond:

Sierpińfinity #1

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Sierpińfinity #2

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Sierpińfinity #3

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Sierpińfinity #4

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Sierpińfinity #5

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Sierpińfinity #6

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Sierpińfinity #7

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Sierpińfinity #8

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Sierpińfinity #9

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Sierpińfinity #10

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Sierpińfinity (animated)

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Here are some more fractals created from three lines of the dissected diamond (sometimes the fractals are rotated to looked better):

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And in these fractals one or more of the lines are flipped to create the next stage of the fractal:

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Previously pre-posted:

• Fractangular Frolics — fractals created in a similar way

• Dissecting the Diamond — fractals from another kind of diamond