Choose a symmetry type and a base shape. The canvas repeats your choice around the center. Switch to freehand mode and every stroke mirrors across fold lines.
Rotational symmetry uses Cn notation: C4 means four identical copies around a full turn. Point groups combine rotation with reflection; D4 gives you fourfold rotation plus four mirror lines. Wallpaper groups describe how 2D patterns repeat across a plane. There are exactly seventeen.
This tool previews the visual result. For strict group-theory notation or crystallographic classification, textbooks and specialist software handle the formal mapping.
The Geometric Pattern Generator offers radial modes and mandala rings with more depth control. The Tessellation Generator focuses on tiling and edge matching. If you need grammar-driven fractals, the L-System Visualizer lets you edit axioms and productions.
Custom draw here applies your chosen symmetry to every stroke. You do not get separate layers or undo history. Export a PNG when the result looks right.
Short answers for classroom and hobby use.
Each point you draw gets transformed by the active symmetry. The path is not stored and then mirrored as a whole. You draw and see the mirrored result immediately. For full-path mirroring, use a shape mode.
Reflectional draws both the original and its mirror across each axis. Point group combines rotation and reflection so you get both rotational copies and reflected copies. Point group usually produces denser patterns.
No. This tool outputs a raster PNG. For vector output, trace the PNG in Inkscape or a similar app, or use a dedicated vector symmetry tool.
Fold lines overlay the pattern. Redraw replaces the canvas contents, so the overlay goes away. Toggle Fold lines again after redrawing to show the axes.
Reviewed March 2026. Symmetry modes are preview engines, not formal group-theory implementations.
