Artin–Tits Word Game — Public Sandbox (v4)

Artin text prototype Main:

Select subword: click a letter (selects a 1-letter subword), or drag from gap to gap in the same MAIN/WORKSPACE word (selects the subword between them). Emergency: click a gap, then Shift‑click another gap in the same word (forward direction, allows wraparound).
Inverse occurrences in tiles/workspace highlight (red). Click a highlighted occurrence to apply the relation.
Insert: click a gap in MAIN/WORKSPACE (blue line), then click a gap in a TILE/WORKSPACE word to insert (the inserted word is rotated to start after its chosen gap). Rotate: drag any letter left/right. Workspace: double‑click to create an empty word (circle). Drag words by the ⠿ handle; click that handle to select a word for Duplicate/Delete. Clear: click blank space in the workspace or below the main word.

Sandbox

Explore words freely. You can mix manual moves with the inverse‑pair algorithm (Hint / Apply hint / Apply algorithm) to hunt for identity words. Use Save to keep intermediate words so you can combine them later.

Algorithm

steps

Tip: you can still rotate, insert tiles, commute c/d via Reduce main, etc. between algorithm runs.

Saved words

Random word generator

Generates a random word in a,b,c,d,A,B,C,D. Letter weights are normalised automatically.

length P(a) P(b) P(c) P(d) (n−2)-bias p colour-bias q start colour

Preview:

(none)

Word inverter

w^{-1}:

Algorithm replay (test word)

Enter any word and watch the inverse‑pair algorithm (goal‑stack) try to reduce it without ever increasing length. Use ←/→ to step through inverse‑pair choices and subgoal stacks. Rotation uses the current Rotation toggle (↻).

Word: Algo:

Suggest puzzle

Suggestions are only accepted if the algorithm reduces the word to empty and it looks “interesting” by simple thresholds. (This public build stores suggestions locally and lets you copy a JSON payload to submit elsewhere.)

Word:

Create mode

Enter a starting word v (leave blank for the empty word) and decide whether rotation is allowed while solving. Then play with the word using the usual moves. When you reach a word w you like, use the buttons below to create a puzzle.

Start word v:

Level: allow algorithm Note (optional):

Goal-based puzzle (start v)

Choose goal constraints that the current word w satisfies, and create a puzzle starting from v. The puzzle will be accepted only if the current word satisfies the chosen goals.

eliminate a/A eliminate b/B eliminate c/C eliminate d/D length ≤

Manual input

Add a puzzle directly. If you provide a target word, the goal is to reach that target. Otherwise the goal is the conjunction of the chosen constraints (default: reduce to empty).

Start: Target: allow algorithm

eliminate a/A eliminate b/B eliminate c/C eliminate d/D length ≤

Auto‑generate puzzles (experimental)

This tries to generate identity words that are not quickly reduced by a simple “two‑move lookahead” shortening heuristic. It is deliberately heuristic/non‑deterministic, so you may want to click “Generate” a few times.

Base length Base word (optional) Omit letter Bias p (match i−2) Colour bias q (same as previous) forbid same generator twice Random reductions left‑priority right‑priority Easy‑test steps Reduction depth Min puzzle len Batch show reduction stats

Puzzle solved!

Replacement:

Workspace (double‑click to create an empty word; click empty space to clear highlighting). Also: click blank area below the main word to clear.

Level: allow algorithm

Start word

Use letters a,b,c,d and A,B,C,D (caps = inverses).

Target word (optional)

If non-empty, the goal is to reach this exact word. If blank, the goal is given by the goal constraints below (default: reduce to empty).

Instruction (optional)

Shown in play mode. If blank, the app will still show the goal constraints.

Goal constraints (conjunction)

eliminate a/A eliminate b/B eliminate c/C eliminate d/D length ≤

Tip: In the sandbox, you can interleave manual moves with the algorithm. Save intermediate words and recombine them.