Julia.Julia Class Reference

Julia is a tool built for generatinpythg various julia sets. More...

Public Member Functions
def	plot_all_sets_on_the_eulers_spiral (self, resolution_in_time, cmap, path)
def	plot_all_sets_on_spiral (self, resolution_in_time, cmap, path)
def	color_map_PIL (self, itterations_til_divergence)
	Apply some sort of mapping from the number of itterations the point in the complex plane does before diverging to an RGB value that the pixel will take on. More...
def	plot_with_PIL (self, dir='./', phase='')
	Function used to render an image of the specific julia set defined by the constant value given by the user using to PIL library. More...
def	plot_julia_set_with_matplotlib (self, cmap, step_number, path)
	Function used to render an image of the specific julia set defined by the constant value given by the user using to matplotlib library. More...
def	plot_mandelbrot (self)
	Plot but for the Mandelbrot use case. More...
def	set_resolution (self, resolution)
	User accessable function that allows them to set what resolution to set the generated photo.
def	set_constant (self, c)
	Function enabled to let the user set the constant value of the constant that is used in the itterative definition of the set.
def	set_color_map (self, cmap)
	Function enabled to let the end use set the color map they like best. More...
def	plot_all_sets_on_the_unit_circle (self, resolution_in_time, cmap, path)
	Define a unit circle, transcribe it in the complex plane, and find all of the julia set for all of the value. More...
def	plot_some_sets_on_real_number_space (self, resolution_in_time, cmap, path)
	Define a subset 2 -> -2 of the real number space \mathbb{R}. More...
def	plot_some_sets_on_imaginary_number_space (self, resolution_in_time, cmap, path)
	Define a line in the complex plane ranging from 2 to -2. More...

Detailed Description

Julia is a tool built for generatinpythg various julia sets.

A julia set is defined by a function repeated or itterated numerous time. If due to the starting point the funtion diverges over itteration then the point is said not to be in the set. If remains inside an arbitrary finite space we define then it is said to be in the set.

Note

A Julia set is defined for a point in the complex plane by itterating over the following equation. If the Z value blow up beyond a certain magnitude then we exclude it from the set. However, if it stays arbitrarily finite then we in clude it in the set

https://www.desmos.com/calculator/n1698xdz63

Znext = Zprev * Zprev + constant 

• where c is a constant we define in the complex plane or in any arbitrary 2D vector space if you are thinking about it graphically

Member Function Documentation

color_map_PIL()

def Julia.Julia.color_map_PIL	(		self,
			itterations_til_divergence
	)

Apply some sort of mapping from the number of itterations the point in the complex plane does before diverging to an RGB value that the pixel will take on.

Parameters

itterations_til_divergence

array of measurement of how many iterations each point lasted untill it diverged

Todo:

fix spelling mistake

plot_all_sets_on_the_unit_circle()

def Julia.Julia.plot_all_sets_on_the_unit_circle	(		self,
			resolution_in_time,
			cmap,
			path
	)

Define a unit circle, transcribe it in the complex plane, and find all of the julia set for all of the value.

Parameters

resolution	number of steps in time/phase to take along the unit circle
cmap	color map to plot the rotation as

plot_julia_set_with_matplotlib()

def Julia.Julia.plot_julia_set_with_matplotlib	(		self,
			cmap,
			step_number,
			path
	)

Function used to render an image of the specific julia set defined by the constant value given by the user using to matplotlib library.

Note

For a more detailed explaination of what a Julia set is please see - https://youtu.be/dctJ7ISkU-4

Parameters

dir	directory the file should be saved in
phase	current phase in radians of where the constant value is regards to the unitcircle

plot_mandelbrot()

def Julia.Julia.plot_mandelbrot

(

self

)

Plot but for the Mandelbrot use case.

Note

For explaination of what the Mandelbrot Set is see - https://youtu.be/NGMRB4O922I

Benoit Mandelbrot is a recent enough mathematician for you to find his Ted Talk on youtube: https://www.youtube.com/watch?v=ay8OMOsf6AQ

plot_some_sets_on_imaginary_number_space()

def Julia.Julia.plot_some_sets_on_imaginary_number_space	(		self,
			resolution_in_time,
			cmap,
			path
	)

Define a line in the complex plane ranging from 2 to -2.

Then find every corresponding julia set on that line.

Parameters

resolution_in_time	- degree of resolution that the line should have. number of steps is equal to resolution_in_time times four
cmap	- color map
path	- file path and naming convention to store the files.

plot_some_sets_on_real_number_space()

def Julia.Julia.plot_some_sets_on_real_number_space	(		self,
			resolution_in_time,
			cmap,
			path
	)

Define a subset 2 -> -2 of the real number space \mathbb{R}.

Then find all of the julia sets for all of the values

Parameters

resolution_in_time	- parameter setting how many increments to take on the path
cmap	- matplot lib color mapping to apply
path	- path and naming convention to store the files

plot_with_PIL()

def Julia.Julia.plot_with_PIL	(		self,
			dir = './',
			phase = ''
	)

Function used to render an image of the specific julia set defined by the constant value given by the user using to PIL library.

Note

For a more detailed explaination of what a Julia set is please see - https://youtu.be/dctJ7ISkU-4

Parameters

dir	directory the file should be saved in
phase	current phase in radians of where the constant value is regards to the unitcircle

set_color_map()

def Julia.Julia.set_color_map	(		self,
			cmap
	)

Function enabled to let the end use set the color map they like best.

Parameters

cmap	string refering to which color map we should use supported by the matplotlib library

Options supportted by native matplotlib: afmhot, autumn, bone, binary, bwr, brg, CMRmap, cool, copper, cubehelix, flag, gnuplot, gnuplot2, gray, hot, hsv, jet, ocean, pink, prism, rainbow, seismic, spring, summer, terrain, winter, nipy_spectral, spectral, Accent, Blues, BrBG, BuGn, BuPu, Dark2, GnBu, Greens, Greys, Oranges, OrRd, Paired, Pastel1, Pastel2, PiYG, PRGn, PuBu, PuBuGn, PuOr, PuRd, Purples, RdBu, RdGy, RdPu,
RdYlBu, RdYlGn, Reds, Set1, Set2, Set3, Spectral, YlGn, YlGnBu, YlOrBr, YlOrRd, gist_earth, gist_gray, gist_heat, gist_ncar, gist_rainbow, gist_stern, gist_yarg, coolwarm, Wistia, afmhot_r, autumn_r, bone_r, binary_r, bwr_r, brg_r, CMRmap_r, cool_r, copper_r, cubehelix_r, flag_r, gnuplot_r, gnuplot2_r, gray_r, hot_r, hsv_r, jet_r, ocean_r, pink_r, prism_r, rainbow_r, seismic_r, spring_r, summer_r, terrain_r, winter_r, nipy_spectral_r, spectral_r, Accent_r, Blues_r, BrBG_r, BuGn_r, BuPu_r, Dark2_r, GnBu_r, Greens_r, Greys_r, Oranges_r, OrRd_r, Paired_r, Pastel1_r, Pastel2_r, PiYG_r, PRGn_r, PuBu_r, PuBuGn_r, PuOr_r, PuRd_r, Purples_r, RdBu_r, RdGy_r, RdPu_r, RdYlBu_r, RdYlGn_r, Reds_r, Set1_r, Set2_r, Set3_r, Spectral_r, YlGn_r, YlGnBu_r, YlOrBr_r, YlOrRd_r, gist_earth_r, gist_gray_r, gist_heat_r, gist_ncar_r, gist_rainbow_r, gist_stern_r, gist_yarg_r, coolwarm_r, Wistia_r

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The documentation for this class was generated from the following file:

• Julia.py