Wythoff array

<p>In mathematics, the Wythoff array is an infinite <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> of <a href="/facts/Positive_integer/u65og8JE">positive integers</a> derived from the <a href="/facts/Fibonacci_sequence/mqxpAUQD">Fibonacci sequence</a> and named after Dutch mathematician <a href="/facts/Willem_Abraham_Wythoff/Yvg7cEER">Willem Abraham Wythoff</a>. Every positive integer occurs exactly once in the array, and every integer sequence defined by the Fibonacci recurrence can be derived by shifting a row of the array.
</p><p>The Wythoff array was first defined by Morrison (1980) using Wythoff pairs, the coordinates of winning positions in <a href="/facts/Wythoff%2527s_game/FAc7P5Jz">Wythoff's game</a>. It can also be defined using <a href="/facts/Fibonacci_number/mqxpAUQD">Fibonacci numbers</a> and <a href="/facts/Zeckendorf%2527s_theorem/hg8s2ycr">Zeckendorf's theorem</a>, or directly from the <a href="/facts/Golden_ratio/anloSRmD">golden ratio</a> and the <a href="/facts/Recurrence_relation/JolXC71M">recurrence relation</a> defining the Fibonacci numbers. 
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Wythoff array open-in-new

Wythoff array