Fixed Points of Art and Mathematics: Kandinsky

I opened Google to look for a paper and it showed me a prompt to 'take a look into the life of Vasily (Wassily) Kandinsky'. It's an amazing collection of stories documenting his art, life & legacy. Please take a tour if you have a few minutes over the weekend: 

https://artsandculture.google.com/project/kandinsky 

And, here is one of my favorites, a painting called 'fixed points'. This was drawn in 1942, just a year after the famous 'fixed point theorem' was proposed by Kakutani. 

Incidentally, Kandinsky changed his career in 1896 at age 30 to pursue an artist's career from teaching law and economics. It seems his art remained influenced by Mathematics throughout his life. 

from: https://www.wassilykandinsky.net/work-342.php 

Kandinsky also had a condition called 'synesthesia' (joined perception). He could hear 'colors', that is, associate each note with a specific hue. He once said, "the sound of colors is so definite that it would be hard to find anyone who would express bright yellow with bass notes or dark lake with treble.” 

In fact, he attributed his radical change of career to his experience of Richard Wagner’s composition Lohengrin at the Bolshoi Theatre, that he felt ‘pushed the limits of music and melody’. (“I saw all my colors in spirit, before my eyes. Wild, almost crazy lines were sketched in front of me.”)

p.s. Kakutani's fixed point theorem is not just beautiful, it is enormously important in Economics, esp. in Nash equilibria. It is a generalization of Brouwer's FPT, the one that we were taught in ISI (?): 'A continuous mapping of a convex, closed set into itself necessarily has a fixed point.' Imagine drawing a curve from [0,1] to [0,1] without lifting your pen, it must cross the diagonal line somewhere. Or, in 3-D, imagine trying to comb the hairs on a coconut, there must be a whorl somewhere. 

p.p.s. My math is very rusty, and I apologize for any errors.