The Ulam spiral
If we were to show graphically how prime numbers grow and expand, we’ll see an ever-expanding spiral – a Ulam spiral called after mathematician Stanislav Ulam who discovered it. I extracted my spiral pattern from Adam Freidin’s script on Observable.
That a logical progression of numbers set itself in a spiral-like shape is quite awesome. That from snail shells to Fibonacci & galaxies far far away, all are built after the shape of a spiral is mystifying. The randomness of the unexplained!
What are the chances to align such a pleasant mirror-inverted symmetry in the positioning of these spheres together? Not many according to Lucas Isei’s script: – attr(‘cx’, d => (d.x + Math.random())), attr(‘cy’, d => (d.y + Math.random())) -. For good measure, I used Andy Burnett zoomable tree-map as a backdrop. Treemapping is a method for displaying hierarchical data using nested figures. Fitting!
A random walk sounds like fun. Who hasn’t tried it before?
This is the result of 250 random walks around a 32×31 grid where walks were limited to 3050 steps. And guess what happened? Art having no boundaries – I thanked Jim Kan for setting up the game and walked with the board in a higher (mathematical) dimension!
Jim’s original idea is based on SARSA, an algorithm for learning a Markov decision process. For the more adventurous, I encourage you to visit his page, it is quite impressive – and very colorful too.
In statistics, collinearity is used to predict the association between two variables.
I expanded Mike Bostock’s original tile into a symmetrical inverted pattern to get this design. It may not solve the mathematical problem but oddly, it is reminiscent of the 1960s’ Kinetic art or some of Vasarely tapestry “carton”, minus the color.
Statistic & randomness do have an artistic bent too!