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

Re:Conway's Game of Life, using floating point values instea... by tim_hutton on Friday October 12, 2012 @04:40AM (#4644238)

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 before applying an inverse FFT.

http://en.wikipedia.org/wiki/Discrete_Fourier_transform

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Re:Conway's Game of Life, using floating point values instea... by ghostfish on Friday October 12, 2012 @03:09PM (#4646406)

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.

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Re:Conway's Game of Life, using floating point values instea... by tomrod on Friday October 12, 2012 @10:01AM (#4645046)

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?

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Re:Conway's Game of Life, using floating point values instea... by tim_hutton on Friday October 12, 2012 @11:50AM (#4645539)

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

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