Python program to visualize, listen to and compute various fractal sinusoids.
sinfract.py contains methods to compute three types of functions:
weierstrass: the famous Weierstrass functionbessel: a modified version of it adding ideas from frequency modulation (TODO: explain better)sinfract: a recursive sinusoid (implemented as loop) defined as:
def sinfract(x, a, f, n, k):
if n == 0:
return 0
return a*np.sin(2*np.pi*f*x) + sinfract(x, a/k, f*k, n-1, k)
it should be pretty similar to the Weierstrass function, however it gives funny outputs for instance with s=2.
- install requirements with
pip install -r requirements.txt
- run with
python sinfract-cli.py -anim
This will show an animation of the Weierstrass function.
Try other functions with the --method parameter, like bessel or sinfract. See below for more commands.
- plot a fractal function
- visualize an animation of a fractal function with the
-animparameter - listen to the sinusoids with the
-audioparameter (see below for tips) - as a library, import
sinfract.pyto do what you want!
Since the program needs to generate enough frames for the audio to play, and frequency should be meaningful, a nice place to start is:
python sinfract-cli.py -m bessel -audio -f 256 -fm 1 -beta 1 -p 44100
In general, use -p with a multiple of 44100 to get some seconds of audio.
usage: sinfract-cli.py [-h] [-m METHOD] [-d DEPTH] [-s SCALE] [-p PRECISION] [-start XSTART] [-end XEND]
[-b B_PARAM] [-a A_PARAM] [-f FREQUENCY] [-fm MOD_FREQUENCY] [-beta BETA]
[-audio] [-anim]
sinfract-cli - CLI utility for visualizing and listening to weierstrass functions & friends
optional arguments:
-h, --help show this help message and exit
-m METHOD, --method METHOD
Function to plot. Values:
'weierstrass': classical Weierstrass function
'bessel': modified Weierstrass function,
so that a parameter equals a Bessel function of the first kind with parameter beta,
and b parameter is (frequency+n*fm)^n
'sinfract': fractal sinusoid with amplitude a, frequency f and scale s
-d DEPTH, --depth DEPTH
number of summations to compute
-s SCALE, --scale SCALE
scaling factor, use with sinfract method
-p PRECISION, --precision PRECISION
precision of the x axis
-start XSTART, --start XSTART
starting point of plot on x axis
-end XEND, --end XEND
end point of plot on x axis
-b B_PARAM, --b B_PARAM
b parameter, use with weierstrass method
-a A_PARAM, --a A_PARAM
a parameter, use with weierstrass or sinfract method
-f FREQUENCY, --frequency FREQUENCY
strarting frequency of function, use with bessel or sinfract method
-fm MOD_FREQUENCY, --mod-freq MOD_FREQUENCY
frequency of modulator, use with bessel method
-beta BETA, --beta BETA
beta parameter of Bessel function, use with bessel method
-audio, --audio save wave audio file
-anim, --animate animate plot