Tuhk ja Tolm OÜ

The company

Two kinds of work under one registration

The company is registered in Estonia as 123 Tuhk ja Tolm OÜ, at Tuuleveski tn 16, 10618 Tallinn, and Anni Kiil answers for what it publishes. The name translates as ash and dust, which tells you where the business began.

Software is the other half of it, and the two have nothing in common except an address. An app published here holds no customer records, no orders and no business data of any kind, and has no way to reach any.

How the apps are made

One at a time, small enough to be held in one head. What an app needs to remember goes into its own private folder on the phone, which Android keeps sealed away from everything else installed — no account, no identifier, no analytics, no advertising library.

Which leaves no database to lose, nothing to hand over, and an app that still opens in ten years' time.

Published by Tuhk ja Tolm OÜ

Mustri

A colourwork charting studio

com.kirivark.mustri

A place to design knitting charts, built around the bold geometric patterns of Estonian and wider Nordic folk knitting. Every cell on the grid is one stitch; pick your yarn colours and paint the motif row by row — stars, roses, braids, zigzags, eight-pointed blooms — and watch the band build up as it would on a mitten cuff.

The tools follow how colourwork actually behaves. A symmetry helper mirrors a motif across an axis so borders stay balanced, a repeat preview tiles the chart sideways so you can see the band wrap around, and a stitch count keeps the width in view. Change the palette and the whole chart recolours at once. Everything you make is kept in a personal gallery with its palette and grid, ready to reopen and refine; a library of traditional motif blocks gives you something to start from, and a plain-language guide explains how to read a chart and turn it into stitches. English and Estonian, offline, no account, no advertising.

Mustri on Google Play

Why a band almost never repeats by accident

A band that goes round a cuff has two properties people tend to confuse. The first is arithmetic: a motif of width w only tiles a cuff of n stitches when w divides n exactly — which is why 60 and 72 stitches are such comfortable cast-ons and why a prime number is a trap. The second is rarer than it looks. A band of length n is said to repeat when it is some shorter run copied over and over, and counting those is a classical piece of combinatorics: by Möbius inversion, the number of bands that do not repeat is Σ_d|n μ(d)·k^n/d, for k colours. Subtract, and you get how many patterns of a given width genuinely have a smaller period. The panel does that exactly, in whole numbers.

Stitches around · 24

Yarn colours in the round · 2

16,777,216different bands of this length

6motif widths that tile it (beyond a single stitch)

12widest motif that still repeats twice

4,336bands that do have a smaller period

0.0258%of every possible band

16,772,880that are one-of-a-kind all the way round

Not on this bench: no grid, no motif, no colours and nothing drawn. It never shows a pattern and could not design one. It counts how many could exist, which is a different question and a much easier one.