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.)
That's exactly right! In my simulation quantities like E and J are vectors with x and y components. In contrast B can be thought of as a vector (or bivector, technically) pointing in the z direction, but since it it only has one component it's simpler to just lump it in with the other scalars. (Aside: Having the simulation be in 2D brings in some interesting toplogical restrictions on circuits).
Thanks but I was thinking more about how fields drop off in 2D space versus 3D space. Simple electrostatic example: consider a 1D string of identical resistors. Voltage drops linearly as you go along this string. Now consider a 2D grid of resistors: voltage does not change linearly anymore if you move between two points (current will move in a more complicated spread-out pattern). So the dimensionality changes how fields behave.
Ah, I see what you're getting at. My instinct here is that (exactly as you've pointed out) fields like E and B will fall off like 1/r instead of 1/r^2, but that all of the qualitative behavior will be basically the same. So I wouldn't trust this simulation to predict the precise behavior of a real circuit (even one whose shape was basically planar), but I suspect that it will behave more or less right.
Looking at the examples, it seems like you can make 1D and 2D strings/grids of resistors here in much the same way you would in a 3D model; you just can't make a 3D grid (or non-planar circuits). My general experience working with and teaching basic circuits is that it's rare that we consider current flow in a genuinely 3D medium: the vast majority of problem-solving examples approximate wires as simple 1D paths for charge to follow, and more careful treatments that talk about where charges accumulate to guide current flow around corners, etc. still almost always illustrate their points in 2D diagrams/examples.
So my impression is that this simulation is likely to give a pretty solid qualitative sense of how these systems work, despite its 2D framing.
That's true, but it's actually a property of the circuit. Any circuit that fits into a 2d space will work the same if simulated in 3d: voltage will still drop off linearly along a 1d resistor.
This is because it's actually an emergent property already in 2d space.
Consider a resistor shaped like a capital letter Z in 2d space, with ground at one end and 1V the other. (Assume also that the Z has a square aspect ratio). The potential along the bar in the middle will initially be equal, because all points on the bar are equidistant from our voltage sources (AKA charges) . But the potential will drop along the arms of the Z. So charge will move along the arms and accumulate at the corners, until there is also a voltage drop along the bar, and ohms law holds.
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 )
I recreated Veritasium's setup in my simulator and measured the current through the load resistor, the results of which are here:
https://imgur.com/a/sxVihf0
The gap between the wires is about 1 micrometer, so light should take about 3 fs to propagate through. The simulation output approximately matches this prediction, and over the first few tens of femtoseconds the current increases, with a jump at around 70 fs due to the reflected wave. All of this is pretty much in line with the results of Veritasium's experiment.
Thanks for bringing it up. I might include this as another example in my sim.
I also wonder why the simulator only allows to show E and D fields, and not H and B.
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.)
- Brandon
Looking at the examples, it seems like you can make 1D and 2D strings/grids of resistors here in much the same way you would in a 3D model; you just can't make a 3D grid (or non-planar circuits). My general experience working with and teaching basic circuits is that it's rare that we consider current flow in a genuinely 3D medium: the vast majority of problem-solving examples approximate wires as simple 1D paths for charge to follow, and more careful treatments that talk about where charges accumulate to guide current flow around corners, etc. still almost always illustrate their points in 2D diagrams/examples.
So my impression is that this simulation is likely to give a pretty solid qualitative sense of how these systems work, despite its 2D framing.
This is because it's actually an emergent property already in 2d space.
Consider a resistor shaped like a capital letter Z in 2d space, with ground at one end and 1V the other. (Assume also that the Z has a square aspect ratio). The potential along the bar in the middle will initially be equal, because all points on the bar are equidistant from our voltage sources (AKA charges) . But the potential will drop along the arms of the Z. So charge will move along the arms and accumulate at the corners, until there is also a voltage drop along the bar, and ohms law holds.
[1] https://www.zachtronics.com/kohctpyktop-engineer-of-the-peop...
https://web.archive.org/web/20160305205215/http://www.zachtr...
[1] https://store.steampowered.com/app/1098840/ZACHLIKE/
This really needs a WebGPU port. Multigrid on a GPU is moderately easy.
> (c) Brandon Li, 2025. Ported to Javascript with the help of Paul Falstad.
Can this simulate this?:
"Synaptic and neural behaviours in a standard silicon transistor" (2025) https://www.nature.com/articles/s41586-025-08742-4 .. https://news.ycombinator.com/item?id=43506198
What about (graphene) superconductors though?
Note that my simulation is intended for educational purposes only, not scientific research.
- Brandon
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 .. https://news.ycombinator.com/item?id=39365579
> "Room-temperature quantum coherence of entangled multiexcitons in a metal-organic framework" (2024) https://www.science.org/doi/10.1126/sciadv.adi3147
Electrons (and photons and phonons and other fields of particles) are more complex than that though.
The gap between the wires is about 1 micrometer, so light should take about 3 fs to propagate through. The simulation output approximately matches this prediction, and over the first few tens of femtoseconds the current increases, with a jump at around 70 fs due to the reflected wave. All of this is pretty much in line with the results of Veritasium's experiment.
Thanks for bringing it up. I might include this as another example in my sim.
These are cool _ wave propagation vids too; Nils Berglund wave visualizations: https://youtu.be/v0cZjOIfwos?si=07w2Wd4dPlGmNxHp
_: photon, fluid, standing transverse,, plasma
What about longitudinal waves in plasma, superconductors, and superfluids though? https://www.google.com/search?q=What+about+longitudinal+wave...
I suppose vorticity doesn't matter that much for classical electronic circuits