Tags / Mathematics

 

Fractal Nature of Life

- What are the properties of life?

I do a lot of walking in the countryside, and it was on one such walk earlier this year, that I stopped to take in the vista shown below. It was late autumn/fall, and due to a combination of a hot summer, and recent fine weather, the golden foliage had not fallen as yet. As I allowed myself to become absorbed in the structure around me, I was thinking about how nature creates such rich and beautiful scenes.
Published Nov 27, 2018  10 min read   philosophy · mathematics · artificial intelligence
 

Frequency Analysis of Fractals with Fourier Transforms

- Exploring the characteristics of various fractals using frequency analysis techniques.

Fractals, by definition, have patterns that occur on many scales. This scaling can be in either the time or spatial dimensions. Because patterns repeat, and those patterns occur with different frequencies, due to their scale, they ought to be amenable to analysis by Fourier transforms. Fourier transforms are an efficient technique for decomposing a signal in the time or spatial domain into the frequency domain. So, for example, if a recording of music were put through a Fourier transform, the result would be the musical notes that constituted it, as well as all the harmonics of the instruments that played it.
Published Nov 3, 2018  5 min read   computer science · mathematics