katch wreck`It is also called the #Cantor ternary #function, the #Lebesgue function, Lebesgue's singular function..the Devil's staircase, the Cantor #staircase function, and the Cantor–Lebesgue function. Georg Cantor (1884) introduced the Cantor function and mentioned that Scheeffer pointed out that it was a counterexample to an extension of the fundamental #theorem of #calculus claimed by Harnack.`
sofia ☮️🏴i added a Cantor set sequence as well!
https://opensofias.github.io/celluloid/#amount=16&page=0&neighbors=3&radix=2&seed=~ct5~
#cellularAutomata #cantorSet #proceduralArt #emergentArt #creations
SilverSerpentThe #Cantorset is uuuuh tricky, and now it looks like it's continuum.
The trick was to convert some of the numbers that I found were part of it into ternary number system -- if you do that, you'll find that either the numbers don't have the digit 1 in them, or if they do, then they only got zeroes after it. Daw the Carnor-set on a number line with ternary numbers on it, this becomes more or less evident. So it only excludes the numbers that have a one and then something other than zero after t.
Okay so I w2as asked the question if the #Cantorset is countably or uncountably #infinite.
The Cantor-set is a #selfsimilar #fractal like thingie you get it by taking the interval between zero and one (real numbers), and then, dividing it onto thirds, then erasing the middle third. Then, you take the remaining two thirds, divide them into thirds again and erasing the middle third from each. This goes on for infinity.
And if you scale it up by three, you get two times the stuff. Also countable.