Our firm has been contracted to help a mathematician take his amazing one-million dollar idea to market. Our client specializes in the field of complex dynamics, which, frankly, is well above my pay grade, but so is programming to him. He has a passion for mathematics education and wants to take his programs to the K-12 system to teach middle and high-school students all about the beauty of complex numbers and repeated, tedious calculations. I didn't have the heart to tell him that there are already dozens of websites doing what he wants to do for free; if his inability to use Google keeps us in steady work, who am I to set him straight?
He has created two prototype programs intended for high school math students. He quickly realized that creating user-friendly software is perhaps more difficult than understanding complex dynamics. This is where we come in.
Our contract is to adapt his programs into a complete Programming Systems Product. We must also make it usable by non-programmers, which means that instead of controlling the program by changing hard-coded data within the source code it must accept configuration files from the command-line and adjust its runtime behavior accordingly.
Now, I realize that asking a user to create configuration files and run a program from the command-line is no longer considered user-friendly in the 21st century. We have two teams working on this project: one team will be creating a GUI which is what the students will ultimately interact with. This GUI will drive the core program that you will create. Your responsibility is to make sure that your piece of the Program System adheres to the configuration file format that the GUI team has defined, as well as the command-line interface they are expecting.
Presently, these programs are very simple and self-contained. They are run them directly from the command line:
python src/mandelbrot.py [FRACTAL_NAME]
python src/julia.py [FRACTAL_NAME]
FRACTAL_NAME is the name of a fractal image this program is capable of
producing. When run without this argument the program lists the names of
fractals it can produce and exits.
If you use PyCharm, create a Run configuration to launch the program in this manner.
Next sprint this program will be made to accept the name of a fractal
configuration file from the command-line so that one does not need to hack the
source code each time they want to produce a new image. The GUI team has
translated the hardcoded fractal configurations into the sample configuration
files you will find in the data/ directory. You may disregard these files
in the first sprint of this project.
It is not strictly necessary for you to understand the math behind these fractals in order to refactor this program. The mystery of how so much complexity can arise from iterating a simple formula is what gives it it's appeal.
However, you will feel much more confident about this if you understand at
least a little bit about what's going on. To this end I have provided an
interactive Mandelbrot program called src/interactive.py.
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Left-Clicking on its Canvas will paint a square region using the same algorithm that the
src/mandelbrot.pyprogram uses, except this program will print the values of the Z paramter at each iteration. -
Right-Clicking the Canvas paints the entire image.
Readaing its code and watching its output may help you better understand how your program produces its images.
Important: src/interactive.py is provided for your amusement/benefit.
It is not a part of the assignment, and you are not required to improve it.
UsefulJS does a nice explanation of how the Mandelbrot set works and how the Julia set is related to it:
http://usefuljs.net/fractals/docs/julia_mandelbrot.html
The points inside the cardioid are the points within the Mandlebrot set. These are the coordinates on the imaginary plane corresponding to Z values which fail to become greater than 2+0i after repeated iterations.
You can compare your program's output with other Mandlebrot and Julia set visualizers.
- https://atopon.org/mandel/
- https://sciencedemos.org.uk/mandelbrot.php (note: this program produces images which are upside down relative to our program)
- http://bl.ocks.org/syntagmatic/3736720
- http://usefuljs.net/fractals/
You can find ideas for new fractal configurations by exploring the Mandelbrot
and Julia sets online. You will it helpful to write a small helper program
which converts these websites' (minX, minY), (maxX, maxY) coordinates into
our program's (centerX, centerY) + axisLength scheme. This will also let
you compare your program's output with other working programs.
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FractInt: A classic MS-DOS program (which is still under development!) whose users have made interesting discoveries within the Mandelbrot set and other related fractals over the years
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GNU XaoS: A free and open source fractal explorer for Linux, Windows and Mac
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Eyecandy: Turn your computer into an expensive lava lamp. Contains links to other programs you can use to explore fractals and other interesting patterns of pixels.