Animals Made from 13 Circles (2016)

Another example of constrained creativity is early to mid nineties electronic music.

"While sketching, I kept track of the number of circles I was using, counting one for every curve." After sketching an animal, it should be easier to adjust the image by inserting/removing/moving circles.

Then there is this from his blog --

Dec 2024: Sadly, the Nobel Prize in Physics 2024 for Hopfield & Hinton is a Nobel Prize for plagiarism. They republished methodologies developed in Ukraine and Japan by Ivakhnenko and Amari in the 1960s & 1970s, as well as other techniques, without citing the original papers. Even in later surveys, they didn't credit the original inventors (thus turning what may have been unintentional plagiarism into a deliberate form). None of the important algorithms for modern Artificial Intelligence were created by Hopfield & Hinton. Details in the recent technical report, with lots of references, links, and facts.

https://people.idsia.ch/~juergen/physics-nobel-2024-plagiari...

Those are just the obvious ones that I can immediately spot — there was probably a lot of careful consideration into the placement of circles in order to facilitate good looking arcs and circles that bring the animals to "life".

(1) Listing closed curves by vertices. Each vertex of a painted area is an intersection of two or more circles, and delimits a section of a circle. So the section of circles that enclose a circle can be encoded each by the union of:

(1.1) A circle (index); (1.2) A 2nd circle (index) that intersects the 1st on a first point; (1.3) A bit identifying the (first) intersection (because there may be 2 possible); (1.4) A 3rd circle (index) that intersects the 1st on a second point; (1.5) A bit identifying the (second) intersection.

Note the base circle would be the first intersection of a subsequent section of this closed curve, and the 3rd circle would be the subsequent base circle. So 1/2/3 won't be necessary for subsequent curves. So only (K+2) indices + (K+1) bits are necessary for this encoding.

Total ~K log2(K)+K bits. I hypothesize (left to the reader :)) a closed curve should contain at most 2x13 points. There can be at most 2^13 distinct regions however, so each figure (Animal) can be encoded with less than that many curves per figure. So each figure (Animal) can be encoded with less than 2^13 x 26x(5+1) bits =~ 1.3Mbit.

But that's mostly pathological cases, if each Animal must be a fully connected area, then that might reduce (hypothesis above) to at most only 26x(5+1) bits = 156 bits, or 20 bytes!

I left out a problem which area shapes encoded within each other (like eyes). In that case you need at most another 156 bits per inner cutout shape.

(2) Alternatively, you could use boolean operations to encode each shape. Also left as a fun problem :)

  interface Animal {
    Circle[13] circles();

    // Leftover from Intro to CS, remember to remove
    void make_sound();
  }

But I do think that evolutionary algorithms or MCMC variants could do a better job of this, especially if paired with an auxiliary model for scoring their intermediate results.