algorithm bfs-algorithm dielectric-breakdown-model diffusion-limited-aggregation lichtenberg lichtenberg-figure

Lichtenberg Figures

Currently working on a dielectric breakdown model algorithm. I GOT IT!

This algorithm was developed in an attempt to best simulate the behaviour of an electric current travelling through an inhomogeneous, insulating material following dielectric breakdown.

The folder Source Codes (Attempt 1) contains Python scripts of my first attempt. After working on the single-branch algorithm, I mistakenly implemented depth-first search (DFS) rather than breadth-first search (BFS) for my multi-branch algorithm (I'm no CS major). In the end, my friend Shan Gao helped me develop the final, multi-branch BFS version of this algorithm.

The folder Animations (Attempt 1) contains a few selected animations from certain versions of this first algorithm. Unfortunately, the patterns generated by this algorithm appear unphysical and do not at all resemble Lichtenberg figures.

The folder Source Codes (Attempt 2) contains Python scripts of my latest attempt. For this attempt, I decided to actually read some papers about diffusion-limited aggregation (DLA) and the dielectric breakdown model (DBM). The papers I used as references are mentioned below. I implemented two different algorithms: the single-tree algorithm and the double-tree algorithm.

The folder Animations (Attempt 2) contains a few selected animations from certain versions of this algorithm. The simulations generated by this algorithm are much more realistic and better resemble Lichtenberg figures.

Authors

Acknowledgements

Thanks Andrew! Thanks Oscar! Thanks Sebastian! Thanks Fernando! Thanks Shan! *applause*

Documentation

Hold on, I'm about to get on arXiv!! Nevermind, got rejected :(

Here: Discount Documentation

Real References

L. Niemeyer, L. Pietronero, and H. J. Wiesmann, "Fractal Dimensions of Dielectric Breakdown," Physical Review Letters, vol. 52, no. 12, pp. 1033-1036, 1984.
L. Pietronero and H. J. Wiesmann, "Stochastic Model for Dielectric Breakdown," Journal of Statistical Physics, vol. 36, pp. 909-916, 1984.
A. A. Tsonis and J. B. Elsner, "Fractal Characterization and Simulation of Lightning," Beiträge zur Physik der Atmosphäre, vol. 60, no. 2, pp. 187-192, 1987.

License

GNU General Public License v3.0

Features

Create your own custom grids and choose your own starting positions
Live animations!

That's about it :/

FAQ

Q: Why did you start this project?

A: Because I thought it was cool

Q: Your figures don't really look like Lichtenberg figures...

A: I'm working on it :( Do they now?

Feedback

If you have any feedback, I'd like to hear it! Here's my email: epa058@gmail.com

About

We present an algorithm based on DBM that takes into account the stochastic nature of dielectric breakdown during the formation of Lichtenberg figures.