Monday, 21 December 2009

Fibonacci Fractals

Fibonacci FractalThis fractal's based on the Fibonacci Rose.

The original Rose has two identical interlocking spiral arms. If we delete one of them, we're left with a simple spiral chain of triangles. Each triangle has three sides – one side connects the triangle to its larger parent, one connects it to its single smaller child triangle, and the third side is unused.

Adding child triangles to two sides gives us the fractal – a characteristic cauliflower-shaped branching structure whose adjacent bunches have corners that just touch.

At larger scales, this looks just like one of the family of fractal shapes that we get by using the Golden Ratio to calculate triangle sizes, that let us zoom infinitely far in or out and always get the same shape.

Fibonacci Fractal LimitWith the "Fibonacci" versions we can zoom out infinitely far, but as we zoom in, there's a range where the proportions start to shift perceptibly away from the Golden Ratio, and then, suddenly, the branching sequence hits a dead end, and stops.

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