Search NKS | Online
21 - 30 of 44 for Fibonacci
, Fibonacci[n] , but not r n , Prime[n] or Log[n] .
At stage n the number of polyominoes of each type is Fibonacci[2n - {2, 0, 1}]/{1, 2, 1} .
At step t there are Fibonacci[t+1] states; a given state with m white cells and n black cells appears at step 2m+n-1 .
(e) uses a non-integer base derived from the Fibonacci sequence, with the property that a pair of black cells can appear only at the end of each number.
Note that (d) is the Fibonacci sequence, discussed on page 890 .
In 1202 Leonardo Fibonacci explicitly gave as an example a list of primes up to 100.
.} Length[k]]]]
There are a total of 2 m Fibonacci[m+2] black cells in the pattern obtained up to step 2 m , implying fractal dimension Log[2, 1 + Sqrt[5]] .
Sequence (c) is the powers of two; (d) is the so-called Fibonacci sequence, related to powers of the golden ratio (1 + √ 5)/2 ≃ 1.618 .
In the first case shown, the total number of elements obtained doubles at every step; in the second case, it follows a Fibonacci sequence, and increases by a factor of roughly (1+Sqrt[5])/2 ≃ 1.618 at every step.
The Fibonacci sequence also appears to have arisen in antiquity (see page 890 ).