
The Single Rotation rule: simple and rich reversible cellular automaton (2013) - bemmu
http://dmishin.blogspot.com/2013/11/the-single-rotation-rule-remarkably.html
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sgentle
Fascinating. I notice some arguments that sound a bit like CA applications of
Noether's theorem (symmetries correspond to conservation laws). For example,
"as a consequence of the time-reversibility, no pattern can completely
disappear", and "collision of a lightest spaceship with a static life always
produces another lightest spaceship and the same static life". Could these be
formulated as time-energy and position-momentum relationships?

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jes5199
momentum maps pretty strangely to automata, since to move more slowly you need
a more complicated spaceship

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goldenkey
Thats actually the principle behind doubly special relativity and the Feynman
checkerboard.

If all fundamental particles move at C, then movement at less than C for a
"macroscopic object" would have to be facilitated by internal bouncing.

You can actually get special relativity from a couple principles:

1) All fundamental particles move at C. C usually equals 1 cell per tick.

2) Energy = amount of change per unit time. Change defined as particle
movement or particle interaction.

3) Complimentarity - A particle cannot interact and move at the same time.

4) Mass = amount of internal bouncing

5) Speed of an object = (internal change due to energy / total change due to
energy)

Heres a CA I made based off of these concepts:
[https://github.com/churchofthought/ScatterLife/blob/master/R...](https://github.com/churchofthought/ScatterLife/blob/master/README.md)

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mikhailfranco
Fascinating. The rule reminds me of this iconoclastic tour de force from the
great David Hestenes, which takes intrinsic angular momentum _seriously_ ,
i.e. electrons really are spinning or spiralling:

 _The Zitterbewegung Interpretation of Quantum Mechanics_
[http://geocalc.clas.asu.edu/pdf/ZBW_I_QM.pdf](http://geocalc.clas.asu.edu/pdf/ZBW_I_QM.pdf)

 _" The idea that the electron spin and magnetic moment are generated by a
localized circulatory motion of the electron has been proposed independently
by many physicists. Schroedinger’s zitterbewegung (zbw) model for such motion
is especially noteworthy, because it is grounded in an analysis of solutions
to the Dirac equation. Surely, if the zbw is a real physical phenomena, then
it tells us something fundamental about the nature of the electron..."_

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fallingfrog
This is really cool! It’s very interesting that the time reversible cellular
automata also conserves mass. I feel like there must be a connection to
Noether’s theorem here; in fact I’d wager that _any_ time reversible cellular
automata conserves mass..

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yesenadam
There are a load of papers on the subject, I read a lot a couple of years ago.
Some leading names: Fredkin, Margolus & Toffoli, Gerard Vichniac, Jarkko Kari,
Tetsuya Hattori, Morita & Ueno, Shinji Takasue, mostly 70s and since.

I made movies that looked like sunlight reflecting on ripples in a river (I
mean, looked _exactly_ ) using 2D CA based on a couple of Rudy Rucker papers,
based on (I believe) _the_ original (1D) CA paper, analyzing non-linear
effects on waves, modelled as a row of particles, neighbours joined with
springs, sliding up and down frictionless rods.

I used this super-simple formula to approximate the wave equation: a cell's
height (each cell stores a number representing height of the water) = half the
sum of the 4 neighbours from the previous generation, minus the cell's height
in the gen before that. i.e. C_t=(Nsum_{t-1})/2-C_{t-2}. (Note that adding
C_{t-2} to both sides produces a time-symmetric equation.)

Amazing that it produced totally realistic-looking water! (I added a feature
to show sunlight reflection if the 3D angle of the plane between each adjacent
4 points was in a particular small angle range)

Different conserved quantities in CAs indeed correspond to different conserved
quantities in the physics. (I don't remember the details enough now to say
more.)

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fallingfrog
Thanks, I'll check some of these out! Sounds like a very fun project.

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darepublic
Why not make the gif a graceful fallback instead of showing modern browsers
both svg + low quality gif

