A short story about a “fractal” world

Question

I read this about 15-20 years ago. I suppose it was in some collection, but I don’t really remember. It might well be much older.

In this story, if I remember correctly, all living things are humanoid. But they vary in size in a “fractal” way.

Each humanoid lives in a cubicle, which contains one much smaller cubicle (or just possibly several ones - but I believe just one) inhabited by a smaller version of himself. Crumbs, leftovers from his meal are food enough for the “tenant” (or "tenants" - but as I wrote above, probably just one).

Conversely, his own cubicle (only that one or just possibly several) is contained in the cubicle of a much larger version of himself, and he gets his meal from the leftovers of his “landlord”.

Creatures of different sizes can, and do, communicate, but only if they are at most “one size apart” - and again, probably just with their "landlord" and their only "tenant"

This goes up and down indefinitely, there is no indication of the existence of a largest level, nor of a smallest one either.

I remember very few details. Just something, that looks rather illogical : something said about "art", for the "large sizes" involving hugeness as an artistic criterion, which was not true for "smaller sizes". But though I believe that the word hugeness was the exact term for the artistic criterion, I am not 100% sure.

It is illogical because in a fractal situation like that, every size is at the same time much larger and much smaller than other sizes.

Answer 1

This question reminded me at once of "Love Comes to the Middleman", a short story by David Laidlaw, forming part of his "Middleman trilogy". It is available to read at Laidlaw's website.

The protagonist, Jack, lives in a house intermediate in scale between the smaller "neighborlings" who live in a miniature house on the wall of his bedroom, and the larger "giants" - on whose wall Jack's house is mounted. This universe thus has a recursive, fractal structure, repeating at ever higher (and lower) length scales, as described in the question. A difference with the question, though, is that his neighbors are not copies of Jack, but different individuals, and passing food from one level to the next, although theoretically possible, seems to be done only rarely. One definite point of similarity is that it is essentially impossible to communicate between two levels which are not neighboring in scale - for example, the giants are practically unable to hear the tiny squeaks of the neighborlings.

Jack falls ill with the flu, and one of his samesize neighbors, Liss, comes around to look after him. As she is an artist they discuss questions of art, and in particular how giants are fascinated by the tiny works done at lower levels:

There’s a lot of interest in us, among the giants... They’re intrigued by our perceptions of the world. Do you realize they have to look at our art under micro­scopes?”

Similarly they themselves are intrigued by tiny works done by the beings "three levels lower" than them:

He found himself staring into a construction the size of a rice grain, elaborately carved, a piece of microscopic scrimshaw showing spiral staircases that grew smaller and smaller as they curled toward the center of the grain. On the stairs were incredibly lifelike figures, also dwindling as the steps shrank. Looking at it made him dizzy.

Of course the giants have art too, but it's hard for beings at lower levels to see it. As Liss remarks:

"You have to get way back. We’ve tried scaling it down through the levels, but it loses something. The size is part of the meaning.”