toroidalet wrote:wildmyron wrote:Accidentally found this logarithmic growth whilst looking for spaceships.Code: Select all`sqrt(t) growth`

Adding 1 transition allows for c/2n+1 diagonal wickstretchers, starting at n=3:Code: Select all`<snip> linear growth`

There are quite a few light speed signals and reburnable fuses in this rule. Some examples:

`x = 21, y = 22, rule = B2n3aeij/S01c2n3ack4q5a6e`

o3$b3o$4bo$5bo$6bo$7bo$8bo$9bo$10bo$11bo$12bo$13bo$14bo$15bo$16bo$17bo

$18bo$19bo$20bo$18bo!

`x = 21, y = 21, rule = B2n3aeij/S01c2n3ack4q5a6e`

o3$b3o2$b5o$6bo$7bo$8bo$9bo$10bo$11bo$12bo$13bo$14bo$15bo$16bo$17bo$

18bo$19bo$20bo!

`x = 23, y = 24, rule = B2n3aeij/S01c2n3ack4q5a6e`

bo2$b2o$3o$3bo$4bo$5bo$6bo$7bo$8bo$9bo$10bo$11bo$12bo$13bo$14bo$15bo$

16bo$17bo$18bo$19bo$20bo$21bo$22bo!

I'm certain that there are suitable tail-end reactions to be found in this rulespace which allow for other adjustable speed spaceships.

Majestas32 wrote:Can somebody check the min and max transitions rules?

Do you mean for these diagonal growth patterns?

The sqrt growth works in 2^74 rules: B3aeij/S01c2n3ack4q5a6e - B2i3aceijkqry4aceikntwyz5aceijknry678/S012ceikn34aceijknqtwyz5678

The wickstretchers work in 2^72 rules: B2n3aeij/S01c2n3ack4q5a6e - B2ikn3aeijkqy4aceijknqtwyz5aceijknry678/S01c2cein3aceijkqry4aceijknqtwyz5678

Note that the B2n required for the wickstretchers makes them mutually exclusive.

Edit: It is of course just the reflector for the sqrt growth I used which is incompatible with the wickstretcher. As a double ended sqrt growth it is compatible with the wickstretcher, and works in 2^79 rules: B3aeij/S1c2n3ack4q5a6e - B2ikn3aceijkqry4aceijknqtwyz5aceijknry678/S012ceikn34aceijknqtwyz5678

An alternative reflector allows for a single ended sqrt growth which also works with (but doesn't require) B2n.

`x = 6, y = 6, rule = B2n3aeij/S01c2n3ack4q5a6e`

bo$o$2bo$3bobo$4bo$3bo!

It works in 2^75 rules: B3aeij/S1c2n3ack4q5a6e - B2in3aceijry4aceijkntwyz5aceijknry678/S012ceikn34aceijknqtwyz5678