The Collatz Conjecture
A little fun with maths
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While reading a book called Gödel, Eshcer, Bach I came across the Collatz Conjecture. In mathematics, it is a very fascinating problem because the rules of the conjecture are very easy to state, but so far we have not been able to develop a proof that states whether or not the rules work for all real numbers. I have attached a good YouTube video below that gives a synopsis of the conjecture.
I was interested in this problem because it reminded me of another mathematical wonder, the Fibonacci sequence. The golden ratio is found in many of natures creations, like the skin of pineapples, distributions of leaves on plants, the seed pattern of sunflowers, and even the nautilus shell. I am fascinated how pure mathematics has been found governing evolution and providing the instructions for such seemingly complex organic structures. Yet such complex structures can be described with the utmost simple equations. It is only our inability to experience what we perceive around us as mathematical instructions which cause us to fall into the trap of lost bewilderment about the nature of reality.
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In order to visualize the process the numbers take to make its journey back to 1, I made a simple python script that graphs the iterations on the x-axis and the current value of N on the y-axis. Shown below is the code I wrote as well as the output for the number 27.
You can replicate the code and play with it yourself. Try changing the code to accept float instead of int. This will allow you to input numbers that have decimal point numbers. The theory still works but you will notice that the numbers generally increase in size immensely.