1. divide their sum of squares S by a random uniform(0,1);

2. subtract S; result is T;

3. generate a random unit-length 2-vector then rescale to length sqrt(T).

This is a way to generate two new i.i.d. gaussian randoms from two old ones, plus two uniform

randoms. The algorithm (1+2+3) clearly is more efficient than Box-Muller in the sense no logs are needed. Only divisions and square roots are needed. ]]>

Since you cannot create new cells in Critters, I have to assume that the constructors are fed by periodic streams coming from infinity. (It should go without saying, but this is not “cheating” just using an energy source as we do in the real world).

Here’s an example (in an app I did not write) that copies a recirculating loop of bits into a periodic stream of the same bits. http://dmishin.github.io/js-revca/?rule=15,14,13,3,11,5,6,1,7,9,10,2,12,4,8,0&size=600×200&cell_size=2,2&step=1&rle=51$529b2o36b2o$529b2o35bobo$563bo3bo$564b2o$525b2o44b2o$525b2o44b2o$535bo12bo$536bo9bo$536bo9bo$535bo12bo4$564b2o2$563bo2bo7$5b2o$5b2o3$b2o$b2o$18bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo171b2o$17bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo169b2o$17bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo19bo11bo$18bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo22bo8bo$541bo$8b2o532bo$30bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo$7bo2bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo$7bo2bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo17bo13bo$30bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo20bo10bo$bo6b2o523bo12bo$2bo532bo9bo$535bo9bo$533bo12bo$5b2o564b2o$5b2o564b2o3$529b2o36b2o$529b2o36b2o31$529b2o$529b2o3$525b2o$525b2o That’s one example of signal fanout.

This has wrapped boundary conditions so it eventually crashes into itself.

]]>The machine would be really awesome. I asked recently myself a quite similar question: how does real world living cells deal with the “matter” needed for their replication. ]]>