Message Boards Message Boards

Computational Lichtenberg Figures

GROUPS:

enter image description here

Lichtenberg figures (https://en.wikipedia.org/wiki/Lichtenberg_figure) can be generated by irradiating e.g. PMMA (i.e. Poly(methyl methacrylate), "acrylic glass") with a high energy electron beam. This way electrons are implanted inside the material - which is an insulator. By a controlled discharge very aesthetic tree structures consisting of tracks from the electrical current can be generated. (This is just one method.)

It is fun trying to imitate this using Mathematica! The idea is simple:

  • define a MeshRegion (this is all you need as input);
  • convert it to a Graph (with preserved VertexCoordinates and EdgeWeight);
  • use FindShortestPath to a specific "starting point".

As mentioned there is a simple mapping from a MeshRegion to the Lichtenberg graphics:

enter image description here

The code - a short notebook - comes as attachment. And - due to the universally designed WL functions - it works in 3D without any change of code:

enter image description here

Best regards -- Henrik

Attachments:
POSTED BY: Henrik Schachner
Answer
8 months ago

Very very neat! Thanks for sharing! If I understood correctly: is the front of the white lines equidistant from the starting point?

Now the distance between the lines are set by the mesh-size, how does it work in reality? I presume current is flowing 'everywhere' and due to irregularities in the material or by the geometry you get local maxima of current causing it to heat up and burn the material. I don't see easily what the length-scale is in reality; any thoughts?

POSTED BY: Sander Huisman
Answer
8 months ago

Dear Sander,

thanks for your reply! Well, the animation above was not meant to represent a physical simulation. And in the attached notebook I am calling it "Lichtenberg like figures" - maybe I should have made that point more clear in my post. The white lines shown at a time have the same number of vertexes in common. But I understand the general formation of these figures that the electrons take the shortest path re-using already existing paths from the electrons before. Therefore I made this approach. Another point in question is of course the kind of distribution of the electrons in the material ...

Best regards -- Henrik

POSTED BY: Henrik Schachner
Answer
8 months ago

enter image description here - Congratulations! This post is now a Staff Pick! Thank you for your wonderful contributions. Please, keep them coming!

POSTED BY: Moderation Team
Answer
8 months ago

Wow very nice !! upvoted. will definitely look at your notebook :)

POSTED BY: Ali Hashmi
Answer
8 months ago

Could I know how to creat a such blue line in front-end? Mathematica graphics

I also don't know how to create such gray line in official documentation

Mathematica graphics

POSTED BY: Yode Japhe
Answer
8 months ago

Not using Random Walks to create Brownian Trees?

Aww...

POSTED BY: Michael Gmirkin
Answer
8 months ago

Hi Yode,

you can create such a blue line inside notebooks simply by placing you mouse over a "new line" (when you see that + at the beginning), and then by making a right click:

enter image description here

I regard this as a nice feature and use it quite often. I have no idea about those gray lines ...

Regards -- Henrik

POSTED BY: Henrik Schachner
Answer
8 months ago

Group Abstract Group Abstract