### Real Life Speeds

Posted:

**August 22nd, 2017, 9:26 am**As a continuation of the speed comparison discussion in the Larger than Life thread, I wondered how feasible it would be to make real-life speeds in a cellular automaton.

I figured putting this rule together was a reasonable start:
Spaceships in this rule consist of a state-3 cell with a state-4 cell above it and any number (including 0) of state-2 cells to the right of it.

A 2x1 spaceship is p4, and periods for longer ships increase roughly exponentially with length.

More specifically, if a 2-by-X spaceship is pN, then the next ship's period is 2N - (2X+1).

The first few periods:
The 2x21 ship is our "passenger airline", with a speed of c/1048619 or 286 meters/sec:
2x28 gets you down to just over 1 meter/sec, or a good walking speed:
2x36 (p34,359,738,441) is just a bit slower than a snail, and 2x62 moves about as fast as Mount Everest grows naturally.

Any other methods of compactly creating arbitrarily slow speeds that people can come up with?

I figured putting this rule together was a reasonable start:

Code: Select all

```
@RULE ReallySlow
1 tape ON
2 tape OFF
3 tape advance
4 ticker right
5 ticker left
@TABLE
n_states:6
neighborhood:Moore
symmetries:none
var a = {0,1,2,3,4}
var b = a
var c = b
var d = c
var e = d
var f = e
var g = f
var h = g
var A = {1,2,3,4}
var B = A
var C = B
var D = C
#tape counts up
1,a,b,c,0,0,0,3,d,3
2,a,b,c,0,0,0,3,d,1
2,a,b,c,0,0,0,0,d,3
3,a,b,c,0,0,0,d,e,2
#ticker ticks up
0,0,0,0,a,1,b,4,0,4
0,0,0,0,a,b,0,4,0,4
4,0,0,0,1,A,b,0,0,0
4,0,0,0,a,0,0,0,0,0
4,0,0,0,0,a,b,0,0,0
#ticker ticks down
0,0,0,0,0,0,A,4,0,5
0,0,0,0,0,0,0,A,4,2
A,5,0,b,0,0,0,C,0,2
A,0,5,b,0,0,0,C,0,2
0,0,0,5,a,B,c,0,0,5
5,0,0,0,a,b,C,0,0,0
5,0,0,0,A,B,0,0,0,4
A,5,0,B,0,0,0,0,0,0
```

A 2x1 spaceship is p4, and periods for longer ships increase roughly exponentially with length.

More specifically, if a 2-by-X spaceship is pN, then the next ship's period is 2N - (2X+1).

The first few periods:

Code: Select all

```
x = 21, y = 47, rule = ReallySlow
6.B.B$6.B.B4.D$6.3B4.C$8.B$8.B2$6.3B$8.B4.D$8.B4.CB$8.B$8.B2$6.B.B$6.
B.B4.D$6.B.B4.C2B$6.B.B$6.B.B2$4.B.3B$4.B3.B4.D$4.B3.B4.C3B$4.B3.B$4.
B3.B2$2.3B.3B$4.B3.B4.D$2.3B3.B4.C4B$2.B5.B$2.3B3.B2$2.B.B.3B$2.B.B.B
6.D$2.3B.3B4.C5B$4.B3.B$4.B.3B2$2.3B.3B$4.B.B.B4.D$4.B.3B4.C6B$4.B3.B
$4.B.3B2$B.B.B.3B$B.B.B.B6.D$B.3B.3B4.C7B$B3.B3.B$B3.B.3B!
```

Code: Select all

```
x = 21, y = 2, rule = ReallySlow
D$C20B!
```

Code: Select all

```
x = 66, y = 5, rule = ReallySlow
3B.3B.3B.B.B.3B.3B.3B.B.3B$2.B.B3.B.B.B.B3.B.B3.B3.B.B6.D$3B.3B.3B.3B
.3B.3B.3B.B.3B4.C28B$B3.B.B.B.B3.B3.B3.B3.B.B3.B$3B.3B.3B3.B.3B.3B.3B
.B.3B!
```

Any other methods of compactly creating arbitrarily slow speeds that people can come up with?