My interest is the visualization of data, processes and structures - both real and abstract - with the two-fold aim of making them better understandable and revealing their inherent beauty.
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.