Random design #23. The de Jong Attractor

Strange Attractors are mathematical systems that tend to evolve over time. When drawn with a random set of parameters, the odds of someone else picking the same parameters or getting the same image is 1 in 2^128.

I saved this one so we can compare!

Random design #22 – The Tale of Genji

54 rooms. In each room, a tale of romance, intrigue, and passion at the court of Empress Akiko. No two stories are the same. In front of each door, a unique symbol. Never twice the same either.

The book was written in the early 11th century Japan.

It wasn’t until E Bell’ series of lectures on combinatorics and prime numbers (Bell numbers)  in the early 1900s that we realized the symbols from the Tale of Genji followed the same reasoning on which graph theory, statistic, and stochastic patterns are developed.

Whether to predict a roll of dice, a political race or playing the game of love, stochastic processes have been at the core of our concern to grasp what the future has in store for us for a long long time…

Random design #21

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!

Random  design #20

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!

Random  design #19

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.

Random  design #18

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!

Random  design #17

Neurons interaction in a spiral pattern.

We may not yet understand fully the elements of randomness by which our neuron associate with each other to form a clear thought. One approach is to study the framework in which it happens – linear, circular or other,  and evaluate which pattern works best.

Why is it the first connection that came to my mind once I finished this image was Raphael’s painting “The school of Athens”?  I’ll never know, but that’s the signal my neuron sent me. A lot can be said about thought process & random connections!

Random design #16

Different sizes and perspective of the same original sample of 2 and 6 neurons randomly communicating with each other. The blue tiles – 2 neurons communicating in 2 layers. The tan tiles, 6 neurons communicating in 6 layers.

Not much difference it seems, but there is a nice fractal dimension to it and it makes for a very orderly tiling too!

I guess I should thank Daniel Smilkov and Shan Carter for writing this script for TensorFlow. Good job!

Random design #15

Neural network – the Eldorado of randomness!

This image is a representation of a neural network – thanks to our friends at Tensorflow. Confused? It could be my brain, your brain at work looking at this pictures as thousand – maybe million of our neurons random-connect to each other every millisecond to interpret and make sense of what we see. Not convinced? That’s how AI are been trained to solve problems & be smarter.

A mind is a pretty thing – if we can make sense of it!

Random design #14.

Random was the selection of a Byzantine design from 1856, Owen Jones’ Grammar of Ornament. Random, the reconstructing an 11th-century geometry with tools of 20th-century mathematics, random getting the work completed just in time for the Orthodox Easter celebration.

Random comes in many flavors – this time the conjunction of unplanned for events leading to a significant ending. Happy (Orthodox) Easter all!

And oh yes, I also inserted an element of “graphic randomness” in this image – the background color, size & positioning. The central orb is a real-time image of the planet Mars, courtesy of NASA.

If you’re interested to know more about the design’s geometry and origin, I recommend this article by Conversano and Tedeschini-Lalli for the Journal of Applied Mathematics. Enlightening!