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I've enjoyed Cinderella's story when I first heard it a long time ago. A perfectly fitting shoe, that was almost literally the key to a kingdom, just seemed to me to be a very useful item to have. And when I was first told the story, I hadn't imagined the shoes to be the diamond-like translucent cold bluish-white distant jewelry items that they're typically depicted as in the films. True to a young child's imagination, the shoes of my dreams were rather all colorful inviting things of beauty, almost living magical artefacts. Of a nature more like the stained glass used to tell stories in the windows of churches, or the infinitely changing colored patterns that one can see when looking through a kaleidoscope.
Much more recently, I played around with a later fascination of mine, fractals. When I imagined to recognize the shape of women's stilettos in a random fractal, Cinderella's story came back to me. And I started to wonder what her shoes might have looked like, what her story might have been like, if the fairy godmother had given to Cinderella shoes of ephemeral fractals. That's a story I wanted to explore…
Fractal flames are what I'd consider an own class of fractals, slightly less mathematical and mechanical, with more degrees of freedom (of expression?). When one is seeking good results, they can be fairly computationally intensive. But it's astonishing what kind of computing power is available in the cloud on a temporary basis, for hardly more money than even a well-made wooden shoe would cost, let alone Cinderella's priceless glass ones. Using that compute-on-demand infrastructure, and trying out different widely available software packages, I produced a base set of 1 000 000 (that's one million!) randomly generated fractal flames.
Now, the issue with this kind of almost randomly computer-generated images is that the computer has a hard time telling good from bad quality. Many of the generated images lacked clarity and definition, or attractive features, or were for other reasons just too ordinary to be of much artistic interest to me. But there were true gems in there, too, no doubt about it. Finding a couple good ones by chance was easy. Now finding a significant number of the best ones, that would be a challenge. But lo and behold, AI (artificial intelligence) and its subset, machine learning, have also progressed to a degree that they can be implemented with ease for many use cases. This was one of them. Using a low-code machine learning toolkit, I was after a number of tries and the initial manual categorization of a couple hundred fractals for training purposes able to implement two consecutive image classifying filters. The first one to separate technically bad images from acceptable ones, and the second one to identify truly interesting fractals of all sorts. And gone were over two three quarters of all fractals. These will never see the light of day.
The reduction still left me with well over 100 000 high-quality fractals, to enjoy, to judge, and to use. I first tried to sift through the remaining fractals and be picky about it. Thus, I ended up choosing around 100 items, ones that I really liked for one reason or another. However, 100 was too few, and too many, at the same time. I wanted to show (off) some of my favorites, but I also wanted to show the incredible choice that Cinderella would've had with fractal shoes. To give things an additional twist, I had always imagined Cinderella's dance at court to play out on a checkerboard floor. Obviously not the classic chess 8x8, as this was a grand event with the whole court in attendance, and everyone gliding around on the dance floor like majestic swans. I finally settled for a 32x32 board, thus with 1 024 squares. By far not enough to fit all the courtiers that centuries ago gathered at Versailles, but appropriate for my vision of Cinderella's dance.
On this oversized checkerboard, I strategically placed 32 fractal pieces of my most favored ones. Maybe they're 32 pieces that represent 32 courtiers vying for the King's attention and observing each other? Or is it 32 pieces that represent 32 choices of shoes for Cinderella? Or 32 pieces that represent the visual proximity of 32 colorful images? Or all of those or none? With certainty, 32 pieces that make up only 1/32th of the checkerboard. The reminder of the board, I filled with the help of a custom algorithm, and some manual nudging, taking the fitting pieces from the thousands and thousands of beautiful fractals still vying for my (and the algorithm's) attention. In the end, 1 024 fractals were placed, each separately on its square on the 32x32 checkerboard, but also all together as part of one tapestry telling the tale of another Cinderella, one aware of fractals. You may wonder, where is the tapestry? Patience, all will be revealed, in due time!
And while I did all this coding, running, sifting, sorting and placing, I read up on Cinderella's tale. And realized that the tale that inspired my vision did not originate from the almost contemporary children's movies. They're in fact usually based on a much older tale, put to paper by one Charles Perrault in the 17th century, and called Cendrillon ou la Petite Pantoufle de verre. To pay homage to the Frenchman's tale, this work of art shall become known as Cendrillon.