## Triviality Tester

For scripts to aid with computation or simulation in cellular automata.
A for awesome
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Joined: September 13th, 2014, 5:36 pm
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### Re: Triviality Tester

Rhombic wrote:
A for awesome wrote:Okay, here's something problematic I found with my test 4 prototype:

Code: Select all

rle
To account for extra non-totalistic functionality... do you think it would be possible to re-model test 4 based on a conditional evolution tester, from gaps in the generation number and active cell regions? Many of them will collapse if you remove a crucial spark, but if there is at least one way in which you can separate the oscillator into A and B, with the periods of the cells in the initial oscillator being IDENTICAL to (A+B), then it would be trivial.
NB: this allows non totalistic rules, and the only issues would surely be with the breakup of the oscillators, but this has to be possible anyway.
I believe it would be possible, at least in theory. The problem is handling patterns, such as the following, which have ambiguous separations:

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x = 47, y = 9, rule = B3/S23
45bo$21b2o21bobo$21b2o21b2o$5bo19bo$b2obobo17bobo14b2o$b2ob2o18b2o15b 2o2$ob3obo13bob3obo13bob3obo\$2obob2o13b2obob2o13b2obob2o!

By the way, I solved the problem (at least for non-moving patterns) in my latest versions of nontotalistic apgsearch. Feel free to adapt the code there (it's very similar to that in the demo script I provided).
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce