If you plot of the # of iterations until reaching 1 vs. n, you get this beautiful pattern of points that seem to trace out exponential looking level setspic.twitter.com/1ZqyCkcqOS
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Pick any number n ∈ ℕ.
If it's even, divide by 2
If it's odd, multiply by 3 and add 1
Take the result and plug it back into f(n)
The Collatz Conjecture asserts that every number n ∈ ℕ will eventually result in 1.
This conjecture has remained unproven since 1937pic.twitter.com/PUuLK5L8ms
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Paul Erdős said of the Collatz conjecture: "Mathematics is not ready for such problems."
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We can extend the Collatz function f(n) to the complex plane f(z)
Note that when z is an integer, f(z) is the next term in the Collatz sequence.
f(z) is holomorphic, meaning that we can study its fractal nature (Julia sets) under iterationpic.twitter.com/mFSTPMFg4a
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The Collatz fractal f(z)
The fractal is located on the complex plane
The horizontal line through the middle of the image is the real line
Black regions --> regions of bounded orbit
Other colors--> unbounded orbit
Note the "spikes" at the integerspic.twitter.com/OzMaHdHG5b
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I am so thankful I do not have your job.
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My job is great!
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I never knew that I needed math tweets in my life.
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You TOTALLY need math tweets in your life.
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Also "Godel, Escher, Bach" by Douglas H.
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