Editing 2891: Log Cabin

{{comic
| number    = 2891
| date      = February 7, 2024
| title     = Log Cabin
| image     = log_cabin_2x.png
| imagesize = 353x265px
| noexpand  = true
| titletext = I'm sure the building inspectors will approve my design once they finally manage to escape.
}}

==Explanation==
[[File:log_cabin_golden_spiral.png|thumb|301px|Golden spiral (approximately) overlaid on the floor plan]]

This is a comic featuring a {{w|floor plan}}, presumably of a {{w|log cabin}}, and a pun on the word "log". The odd part about it is the right half, which appears to be infinitely recursive copies of the building, a self-similar {{w|fractal}}. The house as a whole represents a {{w|golden rectangle}} with a side ratio of the {{w|golden ratio}} (phi = 0.5 + (1.25 ^ 0.5) ≈ 1.6180339887...), with successively smaller living areas (further subdivided into rooms, to a common but shrunken and rotated plan) being square adjoined by a golden-rectangle of all smaller living areas in the manner of the areas defined by the classic {{w|Golden spiral}} diagram. The joke is that Randall is intentionally conflating the word "log" in the common phrase "log cabin," where "log" refers to the wood the cabin is made of, with a {{w|logarithmic spiral}}, as "log" is shorthand for "logarithmic".

Every square subunit of the premises consists of a main combined kitchen/lounge area, with an adjoining shower-equipped bathroom, and a hallway leading to a closet and two bedrooms (a double-bed one with en-suite bath-equipped bathroom, and another with a single bed; both having their own walk-in closet space). Between the kitchen and the dining table is the open doorway that serves as the entry into the next inwards level of the floorplan.

A visitor can also walk in a spiral by using the open doorways in the building plan.

In the title text, Randall says that he is confident that building inspectors will approve the design of his log cabin, assuming they can escape. As one moves deeper into the infinite spiral of architecture, the entire log cabin ''seems'' to be a denser labyrinth of rooms and hallways.

It is unknown how the inspectors lost in the inner rooms would shrink in the same ratio, and would only have to head out through the last doorway they walked in through (or two, if they're currently in the en-suite) and then exit each 'main' area in turn until they exited the building itself. If they have any trouble at all (other than rescaling themselves), it would be that there is ''always'' a further inward area that they might consider needs exploring to fulfil their inspection routine. This construction could imply folded spacetime. To perform a correct inspection, the inspectors might need sufficient relation that inner rooms are identical to the outer rooms, and to solve algebraic equations for various parameters.

In any case, though, they would not need to physically enter the floorplan in order to approve the ''design'', so any risk of getting 'lost' would come solely from a psychological inability to break off from the infinite recursion. Approval of ''construction'' would be a different matter. Whether the floorplan could genuinely be infinitely recursive would depend on how Randall has presented it. Typically, these would be submitted as static images (as it is in the comic), in which case at some point there would be insufficient resolution to continue the recursion, effectively ending in a solid pillar. Randall, however, perhaps channeling his inner Black Hat, may have used a program that dynamically generates further levels as you zoom in to the image.

It could have been that the repetition continued outside of what is drawn here, continuing to grow larger as it moves further out, except that only the top-level external entry has a door: the entries to each lower level only have open doorways marked with no door, and except for the clear marking of external windows on the first four iterations, with no internal ones (and therefore no equivalent windows on the subsequent iterations) precludes that possibility. In fact, the first iteration has windows on the 'southern' edge for the single bedroom and seating area, for which there are no equivalents on any of the other iterations.

[https://www.generations-quilt-patterns.com/log-cabin-quilt-block.html Log Cabin] is also a classic quilting block, which starts with a tiny square and spirals outwards.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A drawing of the top view of a log cabin, which includes two beds, a kitchen, a bathroom and furniture. A smaller version of the log cabin is connected to the main building. An even smaller version is connected to the smaller version, and so on, forming a golden rectangle.]

:[Caption below the panel]:
: Log cabin

{{comic discussion}}

[[Category:Engineering]]
[[Category:Math]]
[[Category:Puns]]