I wrote a hypercomputer 60-ish lines of python. It's (technically) more powerful than every supercomputer in the world.

Edit: actually, I spoke too soon. I have written code which outlines a general scheme that can be modified to construct schemes in which hyper computers could possible constructed (including itself). I haven't proven that my scheme allows for hypercomputation, but a scheme similar to could (probably), including itself.

Edit: I was downvoted for this, which suppose was justified.

What my code does is simulates a modified version of CGoL (John Conway's Game Of Life). It's modified so that information can (technically) flow back through time. It's very similar to what EY outlined in the second section of Casual Universes, except my algorithm is much simpler, and faster (it'd be even faster if I hadn't done a half-assed job of coding it and choose a good language to write it in).

My scheme is more general than the code. I've tried explaining it on /r/cellular_automatta here and here, with a passable degree of success.

The scheme itself is capable of hypercomputation with the right underlying rules. I'll write a quick demonstration, assuming you've read Casual Universes, and my explanations

• in order to be capable of hyper computation it must be capable of regular computation. CA have already been proven to be Turing machines in disguise so I'll take this for granted.

• by the above, you should be able to construct a simulation of any turing machine in the CA. Again, this is a fact, so I'll take it for granted

• I've already said that the algorithm involves backwards information flow (time travel by another name)

• by the above, we can construct a state in the CA which simulates a given Turing machine, then pipes it's output back in time to a finite time after the simulation started

• if we modify the simulation to instead just pipe the fact that the machine produce output, and nothing else (one bit), we can know before hand that a turing machine produces output.

I'd think anyone reading this is familiar, but this is called the Halting Problem, I think (I could be wrong, but I am highly confident I am not) my scheme solved it.

The only real problem is that if the T-machine doesn't halt, neither will the one we constructed, but it will produce output after an arbitrarily finite amount of time.

This does mean my scheme is more powerful than an Turing machine. For instance, it can compute the busy beaver function to a proportional amount of values.

You can look at the code here, but it's messily and hacked together. I only wrote it as a proof of concept in the first /r/cellular_automata thread I linked.