September 30, 2014

Building the Collatz Graph in Henshin

The other day I saw an online video about a number-theoretical problem called the Collatz conjecture. The video included some visualizations of the problem which were based on force-directed graph drawing. It was immediately clear to me that such visualizations could be also easily done in Henshin. So I built a minimalistic EMF model and sketched two simple rules:

The first one multiplies x by 2, the second one is the inverse of the 3x+1 rule. Technically, it is not exactly the inverse of the Collatz function, but the conjecture is still true if and only if these two rules can generate every natural number (if we ignore the upper bound in the first rule).
Finally I created an instance model for the initial state and set up a state space. In the following video you can see how to use Henshin's state space explorer to generate the Collatz graph. Have fun. 

1 comment:

  1. PS: also check out GROOVE: