# Re: [Scilab-users] Visualising Collatz sequences

```Hi,

Maybe some hints there:```
```
https://community.wolfram.com/groups/-/m/t/558256

hth

S.

Le 13/04/2022 à 17:36, Lester Anderson a écrit :
```
```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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```
--
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

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