New Sawtooth Patterns
David Bell has constructed two new smaller sawtooth patterns. The first one undercut the size of the previous smallest known sawtooth by 6 cells.
The problem with the 3-engine Cordership is that the 2-engine "wing" component swings wildly in population from small to large, and in the 3-engine Cordership the two (overlapping) wing components are locked together in a non-optimal relative phase, so that whenever one half has a small population, the other half has a large population.
By adding another switch engine in the middle to create two independent wing components, the relative phases can be adjusted in an optimal manner to reduce the population, even taking the extra switch engine into account.
Note: these new Corderships have a smaller minimum population, but the 3-engine Cordership still has a smaller average population. The average population of the 3-engine Cordership is 193.125, whereas the average population of the 134-cell-minimum Cordership is 217.854.
The pattern works in the same way as Bell's previous moving sawtooths, by using the output of c/3 rakes to ignite the blinkers from a c/2 blinker puffer, with the number of blinkers to be consumed growing on each cycle.
Another possible sawtooth design using 'lineship' technology, which Bell has not been able to complete as yet, is presented here.