Colour by Number

A grid of numbered cells and a colour legend. Colour each cell by its number and a symmetric design appears.

What it is

Every cell of the grid carries a number from 1 up; a legend along the bottom pairs each number with a colour. Fill the cells and the picture — a mandala, a mirrored motif, or concentric rings, depending on the page — emerges.

How to use

Work colour by colour or cell by cell; the order does not matter, because each number has exactly one colour. The symmetry means whole quadrants repeat, so the design fills faster than the cell count suggests. Adult and kids pages differ only in grid size and how many colours the legend holds.

Purpose

The colouring lane’s most commercial format, and the fastest-growing adult-colouring niche. It fits the workspace exactly: the design is real generative art — a symmetric field quantised into palette bands, the same quantise-a-field idea lako-contour and lako-flowfield already use — so every seed colours a genuinely different picture rather than a stencil pulled from a library.

History

Colour by number began in the 1950s as a way to teach art fundamentals to children; the 2010s adult-colouring boom made the numbered mosaic a publishing staple in its own right.

This implementation

• Spec knobs: size (10–28), colors (3–9 palette entries), symmetry (dihedral / mirror / radial), cell.
• Generation: a seeded smooth field — two angular harmonics, two radial frequencies, phases — is folded into the chosen symmetry (applied to the coordinates, so the symmetry is exact) and quantised into colour bands over its own value range.
• Guarantee: there is nothing to solve, so nothing to prove unique; instead the page keeps the colouring guarantee the design lane lives by — every cell is a closed region, every printed number maps to exactly one legend colour, and every legend colour is actually used, all checked at build time. The palette is fixed and print-friendly, and the answer key shows the finished, coloured design.