BobO submitted this XKCD (#2891) as a CIDU. I’ve zoomed the image to make the details easier to decipher.
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The “mouseover” or “title” text reads: “I’m sure the building inspectors will approve my design once they finally manage to escape.“
P.S. I’m impressed that Randall Monroe drew each iteration of the square separately, and did not copy/paste anything.
Comics I Don't Understand 
Maybe someone familiar with European paper sizes (like A4) could explain how, if you cut off a square from one size, the non-square rectangular portion left (a golden rectangle) will be the dimensions of the next size down in the official series.
deety is on the right track. The floor plan (for this logarithmic cabin) is laid out in a “golden rectangle”. The floor plan can be rotated and scaled to fit into the “edge” sub-rectangle of the original rectangle. This sub-rectangle can be rotated and scaled to fit into its edge sub-sub-rectangle, etc. The wikipedia entry for “golden spiral” has some nice graphics which are way better than words can describe.
@ deety (1) – That’s not quite how the paper sizes work. The aspect ratio of the “golden rectangle” is around 1.618…, which is longer than the aspect ratio of the paper sizes (√2=1.414…). As demonstrated in the XKCD comic, cutting off a square from a golden rectangle leaves another golden rectangle as the remainder. For the paper sizes, bisecting one size in half produces the next smaller format. A4 paper is 297x210mm, so dividing the long dimension by two (and rounding) produces A5 (210×148). The format series can be extended in both directions (from A0 to A10).
Here’s CGP Grey on metric paper sizes:
XKCD has crossed the “uncanny valley” of comics in that it is so frequently beyond understanding that a website exists solely to explain every issuance (explainxkcd). There are a lot of details that they pick up on that I know I would have otherwise missed.
Thanks for those clarifications re metric paper. Powers’s video was particularly instructive, in its initial, paper-lesson part. The scaling all the way down and all the way up was also a lot of fun, although I wish their YT notes had given references to classic “powers of ten” videos which did this before. This one was certainly worth seeing, both for the difference it makes taking by powers of two instead of ten, and for the bits of science that needed updating.
When I said “classic “powers of ten” videos which did this before” I should have included books, which I think was actually the main early appearances. See for instance https://books.google.com.sg/books/about/Powers_of_Ten.html?id=JX2BQgAACAAJ&redir_esc=y
A classic math joke involving “log cabin” is said to have originated in the novel * Gravity’s Rainbow*. (I can’t do math notation in this editor, so please just imagine or accept it from this plain text.)
(And probably most moderns would write ln instead of log. But that would break the joke.)
It’s Benoit B. Mandelbrot’s house.
Math joke:
Q. What does his middle initial B stand for?
A. Benoit B. Mandelbrot
Q. And what does that middle initial B stand for?
A. Benoit B. Mandelbrot. It’s Benoit B. Mandelbrot all the way down.
@ Danny (8) – “log-cabin + sea = houseboat“
That reminded me of a charming game applet called “Little Alchemy“. You start with the original four “classical” elements (earth, water, air, and fire), and combine them in various ways to make hundreds of other things. Most of the combinations are logical (water+fire=steam), but there are a lot of humorous combinations, too (sword+energy=lightsaber; lightsaber+human=jedi).
I would expect a cabin to be a little more…rustic.
The joke seems to be that the golden rectangle nested forms an approximation of a logarithmic spiral:
golden4.jpg (3000×2000)
So that makes it a “log” cabin.
There’s also the Log Cabin quilt pattern – https://fabric406.com/blogs/fabric406-blog/free-pattern-log-cabin-quilt-block is an example. Start with a small square, sew it to another small square, sew on a strip the length of the two, sew on a strip across the top (or bottom) the _width_ of the square+strip, keep going around until you have a block the size you want. This doesn’t go square like a classic log cabin block, but the spiral is present.
Zbicyclist – Thank you so much – I really want some mandelbrot now! But is 2am and even if there was some place to go and get some and I am not going out. Maybe will suggest to husband that since he always wants to get me a birthday gift and I say “I don’t want anything” (and mean it – something he has learned over the decades) – perhaps I will suggest it to him to buy me some for my upcoming birthday.
@ Meryl (14) – Happy Birthday! — Please let us know whether you did get any almond bread. 🙂
P.S. @ deety – Re: paper dimensions
If you have a design (such as for a paper airplane or origami) that is calibrated for A4 paper, you can produce a substitute by trimming 3/4” from the side of a sheet of US letter (8.5×11”), or alternatively by cutting two inches from the top (or bottom) of a sheet of US legal (8.5×14”) paper. The result will not be the same size, but it will have exactly the same aspect ratio as A4 paper.
No mandlebrot (almond bread), but thank you for asking.