Category Archives: mathematics

All The Stuff You Wished You Knew About Fourier Transforms But Were Afraid To Ask

The Fourier transform underpins so much of our technological lives, in most cases probably without our realising it. The ability to mathematically split a waveform into its frequency components and vice versa underpins much of the field of digital signal processing, and DSP has become an essential part of many electronic devices we take for granted.

But while most of us will know what a Fourier transform is, fewer of us will know anything of how one works. They are a function called from a library rather than performed in themselves. Even when they are taught in schools or university …read more

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Building a Working Game of Tetris in Conway’s Game of Life

If you haven’t been following along with Conway’s Game of Life, it’s come a long way from the mathematical puzzle published in Scientific American in 1970. Over the years, mathematicians have discovered a wide array of constructs that operate within Life’s rules, including many that can be leveraged to perform programming functions — logic gates, latches, multiplexers, and so on. Some of these creations have gotten rather huge and complicated, at least in terms of Life cells. For instance, the OTCA metapixel is comprised of 64,691 cells and has the ability to mimic any cellular automata found in Life.

A …read more

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