readme.md

Chaotic IFS Fractal

This is a Chaotic Fractal generator based upon the work done by Michael Barnsley et alia and is implemented in Numpy. A chaotic fractal is a fractal for which the points are generated by selecting from a collection of vector functions with weighted probabilities.

Dependancies

• matplotlib.pyplt, numpy, pylab, scipy.stats, tqdm, pprint, random, math, sys, time, pylab (optional)

Predefined Transformations: constants.py

• bfern: barnsley fern as researched by michael barnsley
• rose: a conch shell like spiraling rose - a neat constant set found...
• koch: Koch curve (approximate)
• natgalaxy: A galaxy like spiral ascending
• triangle: A serinpenski triangle
• goldenDragon: the golden dragon spiral based off of the golden ratio
• btree: A Symetric Binary tree with no stems scale 0.7 rotation 9 deg
• branch: golden dragon rotated by the angles of the triangle conecting the golden dragon's attractors
• penta: a slice of a branched pentagonal fractal which is a fractal itself
• spentagon:Serenpenski Pentagon
• scarpet: Serenpenski Carpet
• pythagorean: Pythagorean tree note a special d constant is associated with it in the constants.py file
• sfcurve: A space filling curve
• durer: Durer pentagon ...
• antisnow: Koch Anti-Snowflake

Features

• Terminal Interface for configuring a Chaotic Iterated Function System: python ChaoticIFSFractal2.0.py
• Predefined transformations as listed above that can be selected in the terminal interface
• Point Quantity customization

Sample Screenshots:

• Note! Point Quantity based upon calculated point quantity and does not include additional points added withine a threshold of each point so that the data is more dense and displays better ...

• Here is a screenshot of the Golden Dragon Fractal: (1Mil Points)

• Here is a screenshot of the Barnsley Fern (bfern) Fractal: (1Mil Points)

• Here is a screenshot of the Nat Galaxy Fractal: (3Mil Points)

• Here is a screenshot of the Rose Fractal: (1.2Mil Points)

Documentation: ChaoticIFSFractal2.0.py,ChaoticIFSBuilder.py,IteratedFunctionSystem.py

• A lot of the code used here was based on the chaotic fractal code... this is more just an storage than anything else...
• more modular code for rapid testing was the key...

class IFS: (essentially a static class: collection of functions useful for iterated function systems)

method (static)run(self,vector_func,max_points=50000,stop_func=lambda __,_: False,initial_point=np.array([1,1]),status=True)

• generates a sequence of points and returns the x and y values as a tuple containing np arrays for x and y respectivly ex. (np.array([1]),np.array([2]))
• vector_func: takes a np array of two nums and returns a new array
• stop_func: is passed number of points computed and the most recent point and should return true to stop or false to contine
• max_points: is the maximum number of points to compute
• initial_point: is the starting poin defaults to value stated above
• status: logs a progress bar indicating how close it is to finishing...

method (static) affine(self,x_vect,theta=0,stretch= np.array([[1,1],[1,1]]) ,shift=np.array([0,0]))

• Preforms an affine transformation on a row vector name x_vect
• x_vect: the input vector as a numpy array ex. x_vect = np.array([0,42])
• theta: the angle to rotate the input vector by... NOTE: the stretch array can influence rotation too
• stretch: a matrix to stretch the x_vect by
• shift: is added to the x_vect to shift it...

method (static) chaoticAffineGenerator(constants):

• function takes a set of constants as described below and builds a new probabilistic function that selects based on the groups of constants
• returns that new function so it can be used throught other programs (curried function...)
• constants: is essentially a list of functions in the form:

[
    [
    np.array([[a,b],[c,d]]),    #stretch x and y using this matrix
    np.array([h,k]),            #add this to the vector (shift x and y)
    t,                          #rotate the vector by this angle
    p,                          #probability as a fraction that this function is selected
    ]
    ... etc ...
    another set of constants
]

plot(points_tuple,x_name="x",y_name="y",title="Graph"):

• takes input values and plots them as a scatter plot...
• points_tuple: where the first item is a np array corresponding to x values and the seccond item the y values
• x_name: the name of the x axis
• y_name: the name of the y axis
• title: the name title of the graph

method (static) quickAffine(self,x_vect,stretch= np.array([[1,1],[1,1]]) ,shift=np.array([0,0]))

• Preforms an affine transformation on a row vector name x_vect BUT does not explicitly calculate rotation... faster
• x_vect: the input vector as a numpy array ex. x_vect = np.array([0,42])
• stretch: a matrix to stretch the x_vect by
• shift: is added to the x_vect to shift it...

method (static) chaoticQuickAffineGenerator(constants):

• function takes a set of constants as described below and builds a new probabilistic function that selects based on the groups of constants
• returns that new function so it can be used throught other programs (curried function...)...
• gains a speed boost by not calculating rotation by theta...
• constants: is essentially a list of functions .... see chaoticAffineGenerator constants argument