The Fibonacci sequence is a type of quasicrystal in 1-dimension. A quasicrystal

Quasicrystal

A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry...

 is a perfectly ordered material that never repeats the basic structural pattern, and these were discovered by 2011 Nobel Laureate Dan Shechtman

Dan Shechtman

Dan Shechtman is the Philip Tobias Professor of Materials Science at the Technion – Israel Institute of Technology, an Associate of the US Department of Energy's Ames Laboratory, and Professor of Materials Science at Iowa State University. On April 8, 1982, while on sabbatical at the U.S...

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Explanation

A Fibonacci sequence is the result of a recursive iteration, which repeats a structural pattern with a small difference. This aspect of deflationary construction by difference and repetition is also implicit in a quasicrystal. In fact, if we use only two symbols for the starting points of the sequence ( instead of adding numbers ) and form a chain with the same rule, the relation becomes visible.

By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.

In mathematical terms, the sequence F_n of Fibonacci numbers is defined by the recurrence relation

Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms....

with seed values