So these addition formulas that apply to series and parallel resistors seem more generally to be formulas for finding the new ratio when you have several ratios and want to add them together treating the quantity in the numerator or the denominator as equal for all ratios. Series circuits have the same current for each ratio, and differing voltages, while parallel circuits have the same voltage for each ratio and a different current for each. Similarly for these aspect ratios, where you want the new ratio after adding width or height while setting the other (height or width, respectively) equal.

This is neat!

When I was fresh out of uni, I got asked to build a system to show recommendations to people based on a graph of connections between them. I tried to mentally think about these as a network of resistors, which led me to dimensionality reduction and from there to alternating least squares. Isomorphisms are fun like that: they can help you find techniques when you're stuck on something.

If you made the Piet painting from a substrate with constant resistivity, and put wires between each area, you would end up with a working circuit with all the calculated resistances. This then leads to the insight that it doesn't matter how you divide the painting up, its total resistance only depends on its overall size.

You might also find David Ellerman's "Serial Chauvinism" interesting.

https://www.ellerman.org/series-parallel-duality-part-i-comb...

Fun fact: a rectangular sheet of resistor with a specific thickness and terminals at both sides has a resistance unit of: ohms per square. Not square meters, just square!

If you liked this you are gonna like R-2R DAC.

Not all possible Piet Mondriaan-like painting would lead to a valid network, though.

For example if you have a centered square with four identical rectangles organized around in a certain way.

Moreover, even for "valid" paintings, a different network would result from rotating it 90 degrees.

Very fun! I'm always a big of things being viewed as other things—no idea why though!

Ok, if the spatial concept of aspect ratio is the equivalent of electrical resistance, and given the analogy in the article of the painting and the resistor network, what is the equivalence of color then? Frequency?

Part 2:

https://hunsley.io/posts/2024/image-montage-is-resistor-netw...

In the last drawing I noticed the person wrote 2.2k . This is weird for me, for resistors I usually write 2k2 and see others do the same - I also imagine the two red stripes already...

IIUC this is similar to how window layout is computed in systems like qt.

The 3k2 resistor in the Mondriaan network should be 300 ohm, because its height is 3.2 times its width.

Kilovolts? Really?