Misc Math
A collection of scripts related to number theory and quantitative finance.
UlamSpiral.py
This script implements Ulam's Spiral. As the size increases checking for primes will get computationally more expensive and runtime increases in a nonlinear fashion. The picture below shows Ulam's Spiral up to 5 Mio.
Collatz.py
This scripts implements the Collatz's Conjecture. It returns the series, and the primefactors of each elements in the series. As well as a simplified series containing only the odd elements and a graph. Further visualization will follow.
RandomNumber.py
This script is linear congruential pseudo random number generator that generates 100'000 random numbers. After normalizing them into an intervall between zero and one, pixels are with a value of less than 0.5 are drawn black, whereas all the other pixels are left white. That way you can easiliy detect patterns, which depend on the parameters a (multipier) and b (increment).
The formula is a follows: New_Seed = (Old_Seed * a + b) mod m
WienerProcess.py
This script produces vectors with the values that simulate a Wiener process in discretized form. You can define number of processes and and the number of steps per process.
