The Fibonacci word fractal is a fractal curve defined on the plane from the Fibonacci word.
This curve is built iteratively by applying the Odd–Even Drawing rule to the Fibonacci word 0100101001001...:
For each digit at position k:
To a Fibonacci word of length (the nth Fibonacci number) is associated a curve
made of
segments. The curve displays three different aspects whether n is in the form 3k, 3k + 1, or 3k + 2.
Some of the Fibonacci word fractal's properties include:[2][3]
The juxtaposition of four curves allows the construction of a closed curve enclosing a surface whose area is not null. This curve is called a "Fibonacci tile".
The Fibonacci snowflake is a Fibonacci tile defined by:[5]
with and
,
"turn left" and
"turn right", and
.
Several remarkable properties:[5][6]
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Characteristics |
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Iterated function system |
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Strange attractor |
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L-system |
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Escape-time fractals |
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Rendering techniques |
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Random fractals |
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People |
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Other |
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