Intermezzo: Pseudo Random Binary Sequences/Array's

Pseudo Random Binary Array's (PRBA's) (A[i, j], (i < n, j < m), A[i, j] = 0 or 1) are the two dimensional analogon of Pseudo Random Binary Sequences (S[i], i < n, S[i] = 0 or 1) . Primitive polynomials with coefficients 0 or 1 provide the feedback path of shift-registers that are used to generate these maximum length sequences. For a comprehensive introduction see wade94.

PRBA's exist in various sizes and have many useful distinguishing features. The key virtue we use is the "window"-property: eacht bit pattern seen through a pre-discribed window of k-by-l (or larger) bits sliding over the array is unique.
Conversely each k-by-l (or larger) sub part of the PRBA uniquely defines a position in the PRBA.

This figure shows an example of a PRBA (with n = 3, m= 5, k = 2, l= 2). For a more formal treatment of PRBA's we refer to [3].

We have opted to encode a large PRBA (n = 65, m= 63, k = 6, l= 2) through a representation of the 0's and the 1's by two bright colours. A third colour (black in our approach) is necessary to provide distinction between adjacent bits of the same value. The assembled pattern presents a checkerboardpattern when mirrored to a sphere of radius 8 mm (average radius of the human eye).