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A265318

Fibonacci word fractal in an n X n grid, starting downwards from the top-left corner, listed antidiagonally.

1, 0, 2, 5, 3, 0, 6, 4, 0, 0, 7, 0, 0, 0, 0, 0, 8, 10, 0, 0, 20, 0, 0, 9, 11, 0, 19, 21, 0, 0, 0, 0, 12, 18, 0, 22, 0, 0, 0, 0, 13, 0, 17, 23, 0, 0, 0, 0, 0, 0, 14, 16, 0, 24, 26, 0, 0, 0, 0, 0, 0, 15, 0, 0, 25, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 83

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OFFSET

1,3

COMMENTS

The n-th iteration of this curve ends at the n-th Fibonacci number.

As this is not a space-filling curve, not all points on the grid are reached by the curve; these points are given the value 0.

LINKS

Max Barrentine, Table of n, a(n) for n = 1..2484

Alexis Monnerot-Dumaine, The Fibonacci Word fractal, HAL Id: hal-00367972, 2009.

Alexis Monnerot-Dumaine, The Fibonacci word fractal [Cached copy, with permission]

EXAMPLE

The top left corner of the array shows how this curve begins (connect the terms in numerical order):