When spice simulation isn't deep enough... Very educational to show how circuit elements work "under the hood"...for example the LC example doesn't use an L element and a C element as building blocks, but rather it is the two metal plates in close contact which form the bulk of the circuit's capacitance and it is the loop of metal itself which form the inductance.
I don't pretend to know what this simulation is doing, but for the record, electromagnetism works just fine in 2D. You might be thinking "but magnetic fields are intimately tied to cross products, which only work in three dimensions." But you can set up the equations of electromagnetism just fine either using differential forms or bivector magnetism (https://arxiv.org/abs/2309.02548), and it works in any dimension you'd like. (The cross product version is really a narrow and sometimes misleading special case.)
Possibly related: there are options to "View B" and "View H" in the scalar dropdown, not in the vector one. That may be closely related to the fact that in two dimensions, the magnetic field has just a single component. Whether you describe is as a 2-form or a bivector, the magnetic field is an antisymmetric rank-2 tensor: an antisymmetric matrix. In 3D, that means 3 independent components, and there's a one-to-one mapping to vectors (more or less). But in 2D, an antisymmetric matrix has just one independent component. (And in 4D, it's got six: this is precisely the relativistic electromagnetic field tensor, that in 3D splits into an electric part and a magnetic part. My paper has more details.)
On my info page (https://brandonli.net/semisim/info) there's a list of things my simulation can and can't do. After taking a look at the paper you mentioned, I think simulating it may very well be possible, however it might take a bit of effort. As for graphene, its band structure is different enough that I don't think it would work.
Note that my simulation is intended for educational purposes only, not scientific research.
Thanks, quite the useful simulator; I hadn't found that page yet. Additional considerations for
circuit simulators:
What does the simulator say about signal delay and/or propagation in
electronic circuits and their fields? How long does it take for a
lightbulb to turn on after a switch is thrown, given the length of the
circuit and the real distance between points in it?
(I learned this gap in our understanding of electron behavior from
this experiment, which had never been done FWIU: "How Electricity
Actually Works" (2022) https://www.youtube.com/watch?v=oI_X2cMHNe0 )
When spice simulation isn't deep enough... Very educational to show how circuit elements work "under the hood"...for example the LC example doesn't use an L element and a C element as building blocks, but rather it is the two metal plates in close contact which form the bulk of the circuit's capacitance and it is the loop of metal itself which form the inductance.
I wonder how they simulate EM in only 2 dimensions.
I also wonder why the simulator only allows to show E and D fields, and not H and B.
I don't pretend to know what this simulation is doing, but for the record, electromagnetism works just fine in 2D. You might be thinking "but magnetic fields are intimately tied to cross products, which only work in three dimensions." But you can set up the equations of electromagnetism just fine either using differential forms or bivector magnetism (https://arxiv.org/abs/2309.02548), and it works in any dimension you'd like. (The cross product version is really a narrow and sometimes misleading special case.)
Possibly related: there are options to "View B" and "View H" in the scalar dropdown, not in the vector one. That may be closely related to the fact that in two dimensions, the magnetic field has just a single component. Whether you describe is as a 2-form or a bivector, the magnetic field is an antisymmetric rank-2 tensor: an antisymmetric matrix. In 3D, that means 3 independent components, and there's a one-to-one mapping to vectors (more or less). But in 2D, an antisymmetric matrix has just one independent component. (And in 4D, it's got six: this is precisely the relativistic electromagnetic field tensor, that in 3D splits into an electric part and a magnetic part. My paper has more details.)
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Fun. I am reminded of the long forgotten Zachtronics semiconductor game “KOHCTPYKTOP: Engineer of the People” [1]
[1] https://www.zachtronics.com/kohctpyktop-engineer-of-the-peop...
Did you know that archive supports old Flash games like this via the Ruffle Flash emulator?
https://web.archive.org/web/20160305205215/http://www.zachtr...
cefFlashbrowser can do it better
This is also available (with an included Flash emulator, so playable on modern machines) in Zach's free retrospective "Zach-like" [1]
[1] https://store.steampowered.com/app/1098840/ZACHLIKE/
ChipWizard is the updated version and it's in Last Call BBS (from Zachtronics).
Sebastian Lague has been making one of these and youtubing it, the videos are great here's the latest one https://www.youtube.com/watch?v=HGkuRp5HfH8
Note that these are at very different levels of detail. Lague's is at the digital logic level, while Brandon's is some level around atoms/electrons.
Amazing work feels very similar to Paul Falstad page https://www.falstad.com/emstatic/index.html.
This really needs a WebGPU port. Multigrid on a GPU is moderately easy.
The similarity is likely not a coincidence!
> (c) Brandon Li, 2025. Ported to Javascript with the help of Paul Falstad.
Brandon here. I was very much inspired by Falstad's applets. I had him take a look at my simulation and he generously offered to make a JS port.
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Which other simulators show electron charge density and heat dissipation?
Can this simulate this?:
"Synaptic and neural behaviours in a standard silicon transistor" (2025) https://news.ycombinator.com/item?id=43506198
What about (graphene) superconductors though?
On my info page (https://brandonli.net/semisim/info) there's a list of things my simulation can and can't do. After taking a look at the paper you mentioned, I think simulating it may very well be possible, however it might take a bit of effort. As for graphene, its band structure is different enough that I don't think it would work.
Note that my simulation is intended for educational purposes only, not scientific research.
- Brandon
Thanks, quite the useful simulator; I hadn't found that page yet. Additional considerations for circuit simulators:
What does the simulator say about signal delay and/or propagation in electronic circuits and their fields? How long does it take for a lightbulb to turn on after a switch is thrown, given the length of the circuit and the real distance between points in it?
(I learned this gap in our understanding of electron behavior from this experiment, which had never been done FWIU: "How Electricity Actually Works" (2022) https://www.youtube.com/watch?v=oI_X2cMHNe0 )
FWIW, additionally:
Hall Effect and Quantum Anomalous Hall Effect;
"Tunable superconductivity and Hall effect in a transition metal dichalcogenide" (2025) https://news.ycombinator.com/item?id=43347319
ScholarlyArticle: "Moiré-driven topological electronic crystals in twisted graphene" (2025) https://www.nature.com/articles/s41586-024-08239-6
NewsArticle: "Anomalous Hall crystal made from twisted graphene" (2025) https://physicsworld.com/a/anomalous-hall-crystal-made-from-...
From "Single-chip photonic deep neural network with forward-only training" https://news.ycombinator.com/item?id=42314581 :
"Fractional quantum anomalous Hall effect in multilayer graphene" (2024) https://www.nature.com/articles/s41586-023-07010-7
"Coherent interaction of a-few-electron quantum dot with a terahertz optical resonator" (2023) https://arxiv.org/abs/2204.10522 .. > "Room-temperature quantum coherence of entangled multiexcitons in a metal-organic framework" (2024) 2 replies →
The UI is rough but this is very impressive!
This looks exciting, but the images make it look like maybe it's two-dimensional?
So how accurate are the results?
Very clean, educational and informative. Well done, from one Brandon to another!
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im super into stuff like this, takes me back to messing with circuit sims for hours
Really sexy