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Conway's Game of Life, using floating point values instead of integers

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Re: Conway's Game of Life, using floating point values instead of integers

#91

Post by lmm »

andolanra wrote: post #73
mck- wrote: post #69

Earlier quoted context omitted.

Watching this video makes me wonder if Wolfram's "New Kind of Science" is getting old (like Tetris). I was actually reading that book at the book store for hours, getting quite intrigued, but at the same time deterred by its size. Perhaps I should give it another shot some day.

The general criticism of Wolfram's book is that it's heavy on pictures and self-praise and comparatively light on content. It's certainly very pretty, and has some interesting results (e.g. that Rule 110 is Turing-complete) but a lot of the work is summary or rehash of other extant (and often non-cited) material. There are often more thorough, more concise, and more lucid resources on cellular automata from other res…

Note that the proof that Rule 110 is Turing-complete was actually invalid.

(Also, like much of the work in the book, it was written by an uncredited employee rather than Wolfram)

Re: Conway's Game of Life, using floating point values instead of integers

#93

Post by gus_massa »

crntaylor wrote: post #90
Alekanekelo wrote: post #89

Earlier quoted context omitted.

Could you elaborate a bit on your point 1/3? How come the little interest in this subject? Even though it contains no relativistic effects it would seem to have some importance in filling out the complete 'cube' of theories?

The equations you end up with are called the Schrodinger-Newton equations [1]. These are the same as Schrodinger's equation, but with an extra term that couples the wavefunction to a global gravitational field via its mass. I'm not an expert, but possible reasons for the relative lack of interest in these equations include: 1. It doesn't produce many interesting predictions (possible exception: it might be useful for…

There are a few experiments that combine Newtonian gravity and quantum mechanics (1/3).

For example you can split a ray of neutrons, direct each beam throu a different path with different height and then make them collide and see the interference pattern. (The details are in the book of Sakurai "Modern Quantum Mechanics" pp127-129, with data from an experiment of Colella, Overhauser, Werner (1975).)

It is possible to create systems that combine 1/3, but they are almost corner cases and most of the time the other combinations are more useful.

Re: Conway's Game of Life, using floating point values instead of integers

#94

Post by tomrod »

tim_hutton wrote: post #84
ghostfish wrote: post #66

Earlier quoted context omitted.

As far as I'm aware OpenCL performance, while portable, is still somewhat inferior to that of straight CUDA on NVIDIA GPUs, hence my CUDA suggestion. I didn't actually look at the algorithms used in either so I can't comment, perhaps I'll do that tomorrow. What do you mean by using an FFT "for" a convolution? The algorithm is convolving the (presumably 2D) FFT of the game board with a disk filter?

SmoothLife uses two disks around each point to determine the instantaneous rate of change. Inside each disk the values are summed. This is a convolution with a disk filter. http://en.wikipedia.org/wiki/Convolution As it says on that page, FFT is often used for convolution because it is fast: after applying a discrete Fourier transform to the kernel and the image, the resulting images must only be multiplied together…

That's so cool. I love to see real world applications of convolutions.

I wonder if there is an application of Gershgorin's Disc theorem here?

Re: Conway's Game of Life, using floating point values instead of integers

#95

Post by tim_hutton »

jashkenas wrote: post #47

Does anyone have a JavaScript implementation of the paper? It looks like it would be really fun to play with in . Edit Quoth YouTube: "74 minutes on an nVidia GeForce GTX 460" ... maybe not so fun.

Another thing about the 74 minutes. That was for a larger radius than necessary and a smaller timestep than necessary - for a high quality video.

With a radius of 10.0 and a timestep of 0.1 I get 186fps on the same graphics card - visually about the same speed as the youtube video.

Re: Conway's Game of Life, using floating point values instead of integers

#96

Post by tim_hutton »

tomrod wrote: post #94
tim_hutton wrote: post #84

Earlier quoted context omitted.

SmoothLife uses two disks around each point to determine the instantaneous rate of change. Inside each disk the values are summed. This is a convolution with a disk filter. http://en.wikipedia.org/wiki/Convolution As it says on that page, FFT is often used for convolution because it is fast: after applying a discrete Fourier transform to the kernel and the image, the resulting images must only be multiplied together…

That's so cool. I love to see real world applications of convolutions. I wonder if there is an application of Gershgorin's Disc theorem here?

I see something about a circle that contains the eigenvectors of a matrix. How does that apply here?

Re: Conway's Game of Life, using floating point values instead of integers

#97

Post by andolanra »

lmm wrote: post #91
andolanra wrote: post #73

Earlier quoted context omitted.

The general criticism of Wolfram's book is that it's heavy on pictures and self-praise and comparatively light on content. It's certainly very pretty, and has some interesting results (e.g. that Rule 110 is Turing-complete) but a lot of the work is summary or rehash of other extant (and often non-cited) material. There are often more thorough, more concise, and more lucid resources on cellular automata from other res…

Note that the proof that Rule 110 is Turing-complete was actually invalid. (Also, like much of the work in the book, it was written by an uncredited employee rather than Wolfram)

I knew that the proof was actually Matthew Cook's work, but I didn't realize it was invalid. Can you point me to a citation for that?

Re: Conway's Game of Life, using floating point values instead of integers

#98

Post by ghostfish »

tim_hutton wrote: post #84
ghostfish wrote: post #66

Earlier quoted context omitted.

As far as I'm aware OpenCL performance, while portable, is still somewhat inferior to that of straight CUDA on NVIDIA GPUs, hence my CUDA suggestion. I didn't actually look at the algorithms used in either so I can't comment, perhaps I'll do that tomorrow. What do you mean by using an FFT "for" a convolution? The algorithm is convolving the (presumably 2D) FFT of the game board with a disk filter?

SmoothLife uses two disks around each point to determine the instantaneous rate of change. Inside each disk the values are summed. This is a convolution with a disk filter. http://en.wikipedia.org/wiki/Convolution As it says on that page, FFT is often used for convolution because it is fast: after applying a discrete Fourier transform to the kernel and the image, the resulting images must only be multiplied together…

Ah, thanks for the information. I'm familiar with signal processing, so the only way I'm used to seeing convolutions is through the multiplication of FFTs. I wasn't even considering the "regular" way.

Re: Conway's Game of Life, using floating point values instead of integers

#99

Post by lmm »

andolanra wrote: post #97
lmm wrote: post #91

Earlier quoted context omitted.

Note that the proof that Rule 110 is Turing-complete was actually invalid. (Also, like much of the work in the book, it was written by an uncredited employee rather than Wolfram)

I knew that the proof was actually Matthew Cook's work, but I didn't realize it was invalid. Can you point me to a citation for that?

I was thinking of http://science.slashdot.org/story/07/10/29/2212226/wolframs-... ; looking again it seems that's a different proof, apologies.

Re: Conway's Game of Life, using floating point values instead of integers

#100

Post by 33a »

jashkenas wrote: post #47

Does anyone have a JavaScript implementation of the paper? It looks like it would be really fun to play with in . Edit Quoth YouTube: "74 minutes on an nVidia GeForce GTX 460" ... maybe not so fun.

Here you go: http://jsfiddle.net/CSyUb/
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