Hello all, I have prepared a code to generate Collatz sequences based on the even (n/2) and odd ((3n+1)/2) rules.
clear function [ns, seq] = collatz(n) // Reference: https://en.wikipedia.org/wiki/Collatz_conjecture //ns =number of steps; seq=Collatz sequence seq(1) = n; // Position an index on the next element of the sequence i = 2; // Repeat the iteration until you find a 1 while seq(i-1) ~= 1 // Use modulo to define even/odd numbers if modulo(seq(i-1), 2) == 0 // Step taken if even seq(i) = seq(i-1)/2; else // Step taken if odd // seq(i) = 3*seq(i-1) + 1 // "3n+1 Collatz" seq(i) = (3*seq(i-1) + 1)/2; // "shortcut form Collatz" end // Increment index i = i+1; end // Find the length of the sequence ns = length(seq); endfunction n = input('Enter a positive integer: ') tic() for i = 1:n [nsi, seqi] = collatz(i); ns(i) = nsi; seq(1:nsi, i) = seqi; end // Find maxima in each Collatz sequence peak_values = max(seq, 'r') t=toc() mprintf('Elapsed time: %4.8f\n',t) What I would like to try is apply a further rule to generate a plot based on the Collatz sequences using left/right angular turn depending on whether the number is odd or even, going in reverse (starting at 1) and branching out. I can easily define the odd/even numbers in the sequence (modulo), but not sure how to apply the angle rotation for the graphic plot. Any pointers would be helpful. Attached an example image by way of reference. On a secondary point, the Collatz conjecture can be applied to negative values, but would be interested to know how the code has to be tweaked. If you stick a negative value in the code as is, it gets stuck in a loop. Thanks Lester
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