R · plank/knalp\plank/knalpthe word is its own mirror, twice

W1 · source · your words, the accepted wordsstamps

your word	accepted term	what it is
plank	Planck length, 1.616 × 10⁻³⁵ m	the floor of the scale: the length at which gravity and quantum rules weigh the same. every ladder here starts on it.	LIT
knalp	reversal, the mirror image; in time, time reversal	plank spelled backwards. same letters, opposite direction. it's last turn's swap (i ⟷ −i) applied to a word: do it twice and you're back.	LIT
/ and \	mirror delimiters	the two slashes are each other's mirror. as tokens they mark two levels: / is the inner hinge, \ the outer one.	AMBER my level assignment
plank/knalp\plank/knalp	a self-similar palindrome (the pattern W, W again with a new centre: W c W)	23 characters that read the same backwards. the centre is \. each half, plank/knalp, is also a palindrome, centred on /. a mirror made of mirrors. keep doubling it and the centres' depths come out 1 2 1 3 1 2 1 4…, the ruler sequence: the tick marks on a ruler, and the carries of a binary counter.	LIT
self similar	self-similarity, measured by a similarity (fractal) dimension	the part looks like the whole. last turn's I grew once; here every cell the I takes grows the same rule inside itself. how much it fills at each zoom gives a dimension between 1 (a line) and 2 (a full plane).	LIT
kind of	correction taken	last page grew one level. that was the "kind of". this one nests.

W2 · the word · doubled, mirrored, checked–

level–

rule: level 1 is plank/knalp. each level = the last level, a new centre, the last level again. the centre alternates \ and /. level 2 is exactly your string. length at level n = 12·2ⁿ⁻¹ − 1 (11, 23, 47, 95, 191). every level reads the same backwards; the bars above are the depth of each centre, the ruler sequence. LIT

control. the known-bad word plank/plank\plank/plank (no knalp, no mirror) must fail the palindrome check: –

W3 · 1D · the plank ladder, read up and read back down–

level k–

one level of the growth grid is 21 cells across, so each level up is ×21. start on one Planck length and count levels: a proton (1.7 fm) at 15.1, your eyeball (24 mm) at 25.1, you (1.7 m) at 26.5, the Earth at 31.7, the observable universe (8.8 × 10²⁶ m) at 46.7. read upward it's plank; read the same ladder downward, universe to floor, and it's knalp. LIT arithmetic. if you double instead of ×21 (the word's own growth), your eyeball is 110 doublings above the floor and the universe 205.

W4 · 2D · the I grows inside itself · play the word–

Ibound ||someone elseempty

token–

level-1 I cells–

level-2 I cells–

back to the seed after knalp?–

same rule as last turn, one level down: empty → continue, pressure ≥ 2 × fill → take, less → bind ||. plank grows the I forward, cell by cell. / is the hinge. knalp runs the same record backwards until only the seed cell is left, and the page checks every cell is back where it started. \ steps down a level. then plank again: now every cell the I takes has its own 21 × 21 field growing inside it at the same pace, and knalp folds it all back to one. the time line is a palindrome too. LIT (the return is checked, not assumed)

W5 · 3D · three levels stacked · the dimension · what W1–W4 left out–

measuring self-similar. cover the level-2 picture with boxes of side 1, 3, 7, 21, 63, 147 pixels and count the boxes that touch the I. on a log–log plot the counts fall on a line; its slope is the dimension. this seed: –.

the prediction if every level fills the same fraction f of its cells: D = 2 + ln f ÷ ln 21. over 200 seeds f averaged 0.362, so D ≈ 1.67. seed 7 measured 1.63. LIT

only two levels drawn	a 21 × 21 grid of 21 × 21 grids is already 194,481 cells. level 3 would be 85 million, too many for a phone. the rule doesn't change going down; only the picture runs out.	AMBER
true self-similarity	each inner field gets its own random seed, so the inner growths are alike in their statistics, not copies. exact copies would make a perfect fractal; this is the looser kind nature shows (coastlines, lungs).	AMBER my choice
Planck as a real floor	the ladder counts levels from the Planck length, but nothing says space is actually a grid there. it's where our physics stops working, not a measured pixel.	AMBER
the word and the growth	the word gives the schedule (forward, hinge, back, step down, again) and the growth gives the picture. the mirror is exact in both: the word reads the same backwards and the time line returns to the seed.	LIT

small words. write plank, then write it backwards: plank/knalp. that reads the same both ways. now do it twice with a new middle: plank/knalp\plank/knalp. still reads the same both ways. that's a mirror made of mirrors. the I grows the same way: it takes a square, and inside that square a smaller I grows, taking smaller squares. then it all runs backwards, shrinking to one dot, which is exactly where it began.