Hans-Peter Stricker

Even in the supposedly well-understood and seemingly boring realm of multiplication unexpected and beautiful patterns can be found. Multiplication graphs are created by drawing lines from a number x to k·x (mod n) with numbers arranged on a circle. When the numbers k and n are coprime then the function k·x (mod n) acts as a permutation and gives rise to permutation cycles which can be highlighted by color and line width: the shorter the cycle the wider the line. Graphs are arranged in a table (left) and as a sequence (right). Inside each graph and inside the larger structures emerging patterns can be seen and asked for explanation.