Visaulization of Newton's Fractal written in C/C++. This program generates Newton's fractal based on polynomial provided in parameters and saves it to .png image.

1. Requirements
2. How to use
3. Paramaters
   • Polynomial
   • --size
   • --name
   • --zoom
   • --no-saturation
4. How it works
5. Gallery

• Linux (tested on Ubuntu 20.04 LTS)

• g++ compiler

sudo apt intall g++

• ImageMagick

sudo apt install imagemagick

• Basic polynomials understanding :D

sudo learn polynomials

For better expirience i recommend you to watch awesome 3Blue1Brown's video about Newton's fractal and read Wikipedia article.

Download generate file from root directory and call it

./generate "z^3 - 1"

If for some reason it doesn't work you can complie source code localy:

g++ -I/src src/main.cpp src/Complex.cpp -o generate -ldl

and call program as shown above.

To generate fractal you have to provide this argument. Just put it in quotes after ./generate like this:

./generate "z^4 - 1"

az^n

where:

• a is an integer
• z is variable for polynomial (don't change it)
• n is a power of z

./generate "-2z^14 - 2z^2 - z - 9"

./generate "5z^9 + 2z^8 - z^4 - 9"

./generate "-z^5 + 2z^4 - 19z^3 + z^2 - 18z - 2"

You can pick any polynomial as long as:

This is NOT allowed:

./generate "(z - 9)(z + 2)(z - 12)(z + 16)"

This is NOT allowed:

./generate "z^9*2 + 2z^2/8 - z^1/2 - 9"

You can also use tygonometric function like sin, cos, sinh, cosh;

./generate "sin(z)"

./generate "2cosh(z)"

./generate "z^9 - 14z^4 - sinh(z) - 5"

./generate "-4cos(z) + z^8"

For some reason if you pass more than one trygonometric function it get's messy and takes a lot more time to generate, but I'm not smart enough to figure that out :)

Specify desired size of output image.

Default value is 500px x 500px

--size widthxheight

Where width and height are int

Example:

./generate "z^3 - 1" --size 1000x1000

This will generate image of size 1000px x 1000px

Specify name of output image

Default value is Newtons-Fractal

--name name

Where name is string

Example:

./generate "z^3 - 1" --name my_name_for_fractal

This will save the result in my_name_for_fractal.png

Specify zoom of image

Default value is 1

--zoom zoom

where zoom is double

If zoom < 1 image will be zoomed out.

If zoom > 1 image will be zoomed in.

Example:

./generate "z^3 - 1" --zoom 0.1

This will zoom out 10 times.

Example:

./generate "z^3 - 1" --zoom 10

This will zoom in 10 times.

Turn off saturation

All colors won't have shades.

Example:

--no-saturation

Program contains 4 steps:

It takes polynomial provided in parameters and generates code compatible with Complex library and saves it to tmp.cpp.

Then it compiles generated code and creates library called tmp.so

Next step is loading generated library so generator can use functions created by parsing provided polynomial.

Last but not least it generates fractal. If you are interested in how exacly this works I strongly recommend you awesome 3Blue1Brown's video about this topic. Every time different colors are picked, so you can easly say that your fractal is unique😊. When fractal is generated it is saved to .ppm file. For user's convinience it is later converted to .png file and .ppm file is deleted.

./generate "z^4 - 17" --name gallery/1 --zoom 0.7 --size 1920x1080

./generate "-3cos(z) + z^13" --name gallery/2 --zoom 0.7 --size 1920x1080

./generate "-cosh(z) + z^4" --name gallery/3 --zoom 2 --size 1920x1080

./generate "-7z^9 + 14z^7 - sinh(z) + 17" --name gallery/4 --zoom 0.8 --size 1920x1080

./generate "z^6 + z^5 + z^4 + z^3 + z^2 + z + 1" --name gallery/5 --zoom 1 --size 1920x1080

./generate "sin(z) + cos(z) - sinh(z)" --name gallery/6 --zoom 1 --size 1920x1080

./generate "-9sin(z)" --name gallery/7 --zoom 0.1 --size 1920x1080

./generate "cosh(z) - z^20 + cos(z)" --name gallery/8 --zoom 1

./generate "sinh(z) - z^20 + cos(z) - sin(z)" --name gallery/9 --zoom 1 --size 1920x1080