Fibonacci word fractal
The Fibonacci word fractal is a fractal curve defined on the plane from the Fibonacci word. Definition. This curve is built iteratively by applying, to the Fibonacci word 0100101001001...etc., the Odd–Even Drawing rule: For each digit at position "k" : To a Fibonacci word of length formula_1 (the "n" Fibonacci number) is associated a curve formula_2 made of formula_1 segments. The curve displays three different aspects whether "n" is in the form 3"k", 3"k" + 1, or 3"k" + 2. Properties. Some of the Fibonacci word fractal's properties include: File:Fibonacci fractal self-similarities.png|Self-similarities  at different scales. |Dimensions. File:Fibonacci fractal F21 & F20.png|Construction by juxtaposition (1) File:Fibonacci Fractal F22 & F21.png|Construction by juxtaposition (2) | |Construction by iterated suppression of square patterns. |Construction by iterated octagons. |Construction by iterated collection of 8 square patterns around each square pattern. |With a 60° angle. |Inversion of "0" and "1". |Variants generated from the dense Fibonacci word. |The "compact variant" |The "svastika variant" |The "diagonal variant" |The "pi/8 variant" |Artist creation (Samuel Monnier). </gallery> The Fibonacci tile. The juxtaposition of four formula_23 curves allows the construction of a closed curve enclosing a surface whose  area is not null. This curve is called a "Fibonacci Tile". Fibonacci snowflake. The Fibonacci snowflake is a Fibonacci tile defined by: with formula_28 and formula_29, formula_30"turn left" et formula_31"turn right", and formula_32, Several remarkable properties ::