Editing 2891: Log Cabin
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==Explanation== | ==Explanation== | ||
| + | {{incomplete|Created by a TRAPPED BUILDING INSPECTOR APPROXIMATELY PI - HEY, COME BACK H! METERS TALL- Please change this comment when editing this page. Do NOT delete this tag too soon.}} | ||
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[[File:log_cabin_golden_spiral.png|thumb|301px|Golden spiral (approximately) overlaid on the floor plan]] | [[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 | + | 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 opposing terminology mathematical {{w|logarithm function}} shorthand of "log", of which the golden ratio base is a specific case. |
| − | 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 | + | 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 some kind of storage cupboard and two bedrooms (a double-bed one with en-suite bath-equipped bathroom, and another with a single bed; both having suitable walk-in closet space). Between the kitchen and the dining table is the door that serves as the entry into the next inwards level of the floorplan. |
| − | + | 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 door 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. | |
| − | + | 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, 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. | |
| − | + | Alternatively, this may imply that the repetition continues outside of what is drawn here, continuing to grow larger as it moves further out. However, the apparent presence of external windows on the first four iterations, but no internal ones (and therefore no equivalent windows on the subsequent iterations) somewhat belies 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. | [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. | ||
