Fibonacci Arrays (with Tiling Patterns)

摘要

We can use Fibonacci numbers to produce arrays that have finite repeating patterns that are infinite. Each array is constructed from a 2 by 2 'key-box'. The key-box (shown in red) represents the origin integer values used in creating the 2-dimensional array. The key-value sets the upper limit for each array. For example, key 10 sets the limit to 10 where its integer range is 1 to 10; this also fixes the tiling pattern for key 10 (where the key-values are equal to 1, 2, 3, 4, . . . , N). So if we use the digit 9 as our key-value then Array 1 can be created.