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Collatz Tree


The Collatz tree is a visual representation of the Collatz theorem. It is formed using the actual algorithm of the Collatz theorem. The trees stem is the number 1 since as the Collatz theorem states every number will eventually come down to 1. From there the number is multiplied with 2 and a branch is drawn with a slight angle to the right representing the number 2. At the same time each number creates a second branch whith a slight angle to the left representing the number multiplied with 2 and subtracted by 1 and then divided by 3. Of course this second branch is only drawn if the calculation results in a whole number.

Then some colors are assigned to the whole tree showing the branches' actual numbers. Also you can adjust the zoom factor and angle of the tree with your mouse. The algorithm stops once the numbers exceed 10'000.

Click on different places and watch the tree adjust! Vertical for zooming, horizontal for angle.