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I made a script which can create pictures of different mandelbrot and Julia sets. The first document is the original. The second is an upgraded document where color and changes in location are created.
I have taken and changed the code from: https://www.codingame.com/playgrounds/2358/how-to-plot-the-mandelbrot-set/mandelbrot-set
I cannot thank the creator [CG]Maxim enough!
mandelbrot set.pdf∆ window location.pdfSome resultant pictures
infinite_sums.pdfprime_counting.pdf
Primes to 10^2
Primes to 10^2
Primes to 10^4
Primes to 10^4
Even though the amount of primes seem to be following a linear trend this is not true. A quick intuitive check is the proportion of the axes. On the left, the first 100 primes, the ratio between the axes are 1:4 (y:x). On the right though, they change to 1200:10000 or 1:8.33... . This clearly means that the rate of change is decreasing as x gets bigger. It turns out that the distribution of primes follow an approximate trend similar to the pi function. This function, is some sort of parametrised natural logarithm.
Even though the amount of primes seem to be following a linear trend this is not true. A quick intuitive check is the proportion of the axes. On the left, the first 100 primes, the ratio between the axes are 1:4 (y:x). On the right though, they change to 1200:10000 or 1:8.33... . This clearly means that the rate of change is decreasing as x gets bigger. It turns out that the distribution of primes follow an approximate trend similar to the pi function. This function, is some sort of parametrised natural logarithm.
Computing the Fourier series of a function and plotting it
Computing the Fourier series of a function and plotting it
fourier.pdfPage updated
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