josecelano/c-mandelbrot-arbitrary-precision

Proof of concept project about adding arbitrary precision math to Fractal generation software GNofract4D.

About Me

I'm a senior developer with a focus on backend development. My expertise used to be PHP, although I'm also starting to enjoy doing things with TypeScript and I'm now working full-time with Rust. I live in Gran Canaria (Spain) and work remotely.

• GitHub Résumé: https://resume.github.io/?josecelano
• Manfred Profile: https://mnf.red/josecelano

Career highlights

• I'm currently working as a developer on open-source projects, for example: BitTorrent Tracker in Rust.

• From 2016 to 2021 I was working in HYVE as manager and developer. HYVE is a 20-year innovation company located in Munich.

• For a couple of years (2014-2016) I was very involved in Bitcoin projects.

  • PHP wrapper for BlockCypher API
  • Sample Bitcoin wallet in PHP
  • Sample React wallet
  • Bitcoin book reviewer

• I founded a company called iQ Ingenieros together with Emilio Medina. We were building desktop apps with C# and web apps with C# and PHP for 10 years.

• I started working professionally in a gaming company working on a game called Free Wheel (https://www.imdb.com/title/tt1893240/). It was an isometric driving strategy game taking place in a future world inhabited by zombies.

• In 2003 I used a PHP framework called PHP.MVC. It was a port to PHP from the popular Java framework Apache Struts(https://struts.apache.org/). More info about that project (Spanish)

Things I am interested in

• Rust language:

  • BitTorrent Tracker in Rust.

• DDD

  • Symfony DDD sample
  • Laravel DDD sample
  • DDD aggregates experiment using nodejs and zombies

• Fractals

  • Applying "Period Checking" to Mandelbrot set using arbitrary precision. Hosted using K8S on Digital Ocean. The basic library is written in C. Backend with Python and frontend with VUE.
  • Colorized Mandelbrot Orbits. In Rust.

• PHP experiments

  • Arbitrary precision package for complex number in PHP
  • SQL Server console client for Linux in PHP
  • Object literals package for PHP

• Rust experiments:

  • Game of life kata
  • Cargo Pretty Test

• TypeScript experiments:

  • Implement a concurrency lock only with GIT

• Conferences

  • I usually attend Socrates Canaries conference. A Socrates open space conference.

Articles

• Partially verified commits on GitHub
• How to sign commits using the GitPython package
• Import a GPG key using Python
• How to create a single commit with multiple files using GitHub API
• Sign automatic commits in GitHub Actions
• Generating a macOS distributable
• How to deploy Svelte apps to GitHub Pages using GitHub Actions
• DVC: Add Microsoft Azure Blob Storage as remote storage
• DDD aggregates without persistence
• Detecting periodic orbits in the Mandelbrot Set
• MVC pattern (Spanish)
• The Enigmatic Torrent "Source" Field
• Don’t DELETE ON CASCADE
• Containerizing Rust Applications

Tech Guides

• Secure Git Guide
• Testing in Rust
  • Custom mocks in Rust
  • Testing APIs in Rust
  • Static vs Dynamic mocks in Rust

Social networks

• Twitter
• LinkedIn
• Gran Canaria Developers Community
• YouTube - Developer Playlist
• YoutTube- Engineer Manager Playlist

c-mandelbrot-arbitrary-precision's Issues

Create at least one nice color map

There are only 3 color maps implemented:
https://github.com/josecelano/c-mandelbrot-arbitrary-precision/blob/master/src/mandelbrot/domain/image/color_map.h

We could implement at least one more using the number of iterations, for example the one used here:
https://github.com/josch/mandelbrot/blob/master/mandel_mpfr.c

Improve periodicity checking

If you enable "periodicity checking" the application will try to find periods in the fractal loop. The pre-defined periods for the Mandelbrot Set are:

But if you execute the application you will get something like:

The period detection is worse near to the fractal border and and when you zoom in.

That's because there are 3 parameters that are fixed in the algorithm that should be calculated dynamically. These parameters are:

1. Minimum number of iterations before detecting cycles.

2. Period tolerance.

3. Maximum number of iterations.

4. Minimum number of iterations

Param: https://github.com/josecelano/c-mandelbrot-arbitrary-precision/blob/master/src/mandelbrot/domain/optimisation/periodicity_checking.c#L59

The more you are closer to the border the more chaos you will have before the orbit gets stable. For example, this is the orbit for a period 1 next to the main cardioid center:

And this is the orbit for a point closer to the border where the application is not detecting the rigth cycle:

As you can see the orbit get stable after the first 60 iterations and the hard coded value is 20.

2. Period tolerance

Param: https://github.com/josecelano/c-mandelbrot-arbitrary-precision/blob/master/src/mandelbrot/domain/optimisation/periodicity_checking.c#L88

In this image:

you can see a point in the main main circle (period-2) close to the border. You can see the cycle but the peaks are not exactly the same value, you can see there is a difference and the cycle length is not well detected. In this case the problem is we need to adjust the period tolerance. It should be greater.

3. Maximum number of iterations

Param: https://github.com/josecelano/c-mandelbrot-arbitrary-precision/blob/master/src/mandelbrot/domain/optimisation/periodicity_checking.c#L92

This is a point in the main cardioid next to the border.

You can see that tends to a fix value but it takes more iterations than a point closer to the center like:

In order to detect the right cycle length, the application should start detecting the cycle later and increase the number of iterations.

And finally if you want to try different point you can use this site I built to find out how to calculate these 3 parameters dynamically.

https://mandelbrot-set-periods.online/

You can also take a look at this program: https://github.com/fract4d/gnofract4d or any other fractal generation software to find out how to calculate the right values for those parameters.