## Modelling heat as a function of populations and period

For general discussion about Conway's Game of Life.
Rhombic
Posts: 1064
Joined: June 1st, 2013, 5:41 pm

### Modelling heat as a function of populations and period

Firstly, I know many of you will wonder...
Why is this important?
1) When searching for new oscillators with high volatility, it would help to predict what heat is the most probable one from some of the phases of the oscillator by estimating its period. Search scripts could potentially use an optimised version of a formula to do so and increase the efficiency.
2) Potentially, the concept itself could be extended to spaceships and it could help to understand things like the almost-knightship, copperhead, etc. and aid in finding the rest of the small-ish elemental spaceships.

After messing around for a while with SPSS, I devised a formula that gives a very good approximation for the heat of an oscillator based on the maximum population (Pmax), minimum population (Pmin) and period (T) in a way that...

Heat = 0.2048*(Pmax*sqrt(Pmax+Pmin)/(Pmin*sqrt(T)) + 1.1338

No coefficients have been adjusted for the expression itself, which for now I'll call K.
The following list of oscillators fit quite nicely with the expression:

Code: Select all

``````Blinker
Pulsar
Mazing
Octagon II
Fumarole
Figure 8
Achim 8
Blocker
Unix
Caterer
Bent keys
Odd keys
Short keys
``````
Wait, but this won't work for--!
However, as you might already be thinking, there are immediately some problems with this.
The first one is that many oscillators don't fit (like mold, jam, smiley or even beacon).
The second one is that it does not account for a possible non-standard dimension of the stator (mold on cap on cap on cap on cap on cap on cap on table, etc. would fit extremely poorly).

Hence, while the model is a nice first step, I think that there are a few things that have to be addressed to make it useful:
- I'm sure that the reason why it predicts nicely the heat of the oscillators I listed is due to the size of the rotor having a correlation to the populations
- Therefore, if that is true, it would be appropriate to redefine the equation to take into account ONLY the minimum and maximum populations of the ROTOR (or predicted rotor)
- If that is the case, the anomalies for smiley, monogram and queen bee shuttles would be easy to explain, they just seemed "highly unlikely" -- however, it won't explain the case of mold or jam, that's probably down to something else
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
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Rhombic
Posts: 1064
Joined: June 1st, 2013, 5:41 pm

### Re: Modelling heat as a function of populations and period

I have attempted to reconstruct a formula using total rotor size, max rotor population and min rotor population, but it's not as similar to the original expression as I thought. Maybe someone would like to give it a go. An optimised version of the above for the correlation is:

Heat ≈ Knorm = (5.838*Pmax*sqrt(Pmin+Pmax)+132.811)/(30.784+Pmin*sqrt(T))

either way, the deviations with a population-based system will be very significant for oscillators with high volatility, very large stator, etc. But it's a start.
The advantages for the above equation, compared to the one in the previous post, is that for the ~65% of ocillators that fit the trend, this second equation gives a much better prediction of their heat. For the ones that are not properly analysed by the first equation, the improvement is not great except in the case of tumbler or blocker (I can't remember, will update).
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

### Re: Modelling heat as a function of populations and period

Not sure my idea is entirely relevant, but I will post it here.

My approach would be to model heat as a fluctuation in density. Simply record the density at the different timepoints, and find a way to quantify them. I found this idea very useful when trying to classify the CA rulespace.

Density can be measured quite arbitrarily. Say you get a time sequence of 000110010110, then I can chop this up into trimer: 000,110,010,110. Depending whether we take permutation symmetry or circulation symmetry only, we can treat them differently.
e.g.: In permutation symmetry, 1010 is same as 1100 , but circulation symmetry only allows 1010 to equal to 0101. One would also consider how to treat on/off symmetry. For simplicity, we take permutation symmetry here, so that we can take arithmetic average safely
000-> 0
110-> 0.666
010-> 0.333
110-> 0.666
Now we have grouped original CA snapshots into group of 3 consecutive pieces, at an interval of 3 timesteps (although I use 6 in practice). It's now possible to derive temperature from this parameter. The way I use it is to derive global 2-point correlation between 2 timepoints of a CA-trajectory to define the dynamics of a CA, but I imagine you can use it differently. The good thing about this parameter is it collects information about local environment of a cell before any more treatment.

Hope I haven't been too confusing.

Kind regards
Feng

Rhombic
Posts: 1064
Joined: June 1st, 2013, 5:41 pm

### Re: Modelling heat as a function of populations and period

shouldsee wrote:Not sure my idea is entirely relevant, but I will post it here.

My approach would be to model heat as a fluctuation in density. Simply record the density at the different timepoints, and find a way to quantify them. I found this idea very useful when trying to classify the CA rulespace.
It is an idea that would almost certainly yield better results. However, I'm not sure about how well this would be applicable for oscillators with undefined rotors - this is meant to be an aid in guiding as to what heat to accomplish (as in the construction of a potential xp19).
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?