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A new type of random permutations generator to simulate random images. (English)
Comput. Stat. Q. 6, No.1, 55-64 (1990).
Let \$k=1,2,3,... \$. Write for relatively prime \$q\sb 1,q\sb 2,...,q\sb r\$ \$s(k)=k\sb 0+k\sb 1q\sb 1+k\sb 2q\sb 1q\sb 2+...+k\sb rq\sb 1q\sb 2...q\sb r,\$ where \$k\sb j=k(mod q\sb{j+1}).\$ s(k) does not define any good random sequence. Let \$n=q\sb 1q\sb 2...q\sb r=q’\sb 1q’\sb 2...q’\sb r\$ be two decompositions of n into the products of relatively prime numbers. Then using the above given turn we obtain two functions s and \$s’\$. We can define \$s\sb 2(k)=s’(s(k)).\$ This turn can be repeated. The permutations \$s\sb t\$ were not excessively statistically tested, but they were used to generate two-dimensional patterns strongly resembling the patterns of the structure of granite stones. The algorithm of pattern generation is given and some of its statistical properties are proved. The algorithm uses decision functions. Examples of patterns generated by the algorithm are given.
Reviewer: J.Král (Praha)
Classification: 65C10