Free Radial Grid Maker

The spoke count is the more consequential of the two settings, because it fixes the symmetry of everything you will subsequently draw. Once you have chosen twelve, the design has twelve-fold symmetry and every motif has to work twelve times round. Change it later and the whole thing is redrawn.

Twelve is the count traditional ornament reaches for most often, and there is a good structural reason: twelve contains two-, three-, four- and six-fold symmetry simultaneously. A twelve-spoke framework will support a motif in any of those folds without a second grid, which is exactly what a rose window or a mandala needs when its elements sit at different scales.

Eight is the next most common, and it is what you get from repeated halving: a circle, its two axes, then the diagonals. That is a construction achievable with a compass and straightedge in four moves, which is most of why octagonal rosettes appear in every tradition with a compass.

Five and ten are the difficult ones. A regular pentagon is constructible with compass and straightedge, but the construction is long enough that most traditions either avoided it or approximated it — which is one reason five-fold ornament is comparatively rare and, where it appears, tends to signal a sophisticated workshop.

Fifteen of the counts available here divide 360° into whole degrees: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30 and 36. If you are going to transfer the design by protractor, choosing one of those makes every measurement exact rather than approximate. Seven, eleven, thirteen and their relatives do not divide evenly, and while the overlay draws them accurately, you will not be able to measure them off a protractor.

Seven-fold is worth a note because it is the classic hard case. It cannot be constructed with compass and straightedge at all — a result that follows from Gauss's work on constructible polygons — so every historical seven-fold rosette is either approximate or was laid out by a method other than pure construction.

The rings are the other half. They are spaced at equal steps in radius, and it matters to know that this is not the same as equal steps in area. With six rings, the bands they enclose have areas in the ratio 1:3:5:7:9:11, so the outermost band is eleven times the area of the innermost disc.

The radial and circular overlay page covers that history, beside the rest of the specialty grid category. Historically, the radial figure is close to universal. The mandala in Hindu and Buddhist practice is the most systematised form — a cosmological diagram with a strictly defined structure of concentric enclosures and cardinal gates, laid out on exactly this grid. The Kalachakra sand mandala is constructed from the centre outward over days, with the grid snapped in chalked string lines before any coloured sand is placed.

The Gothic rose window is the same construction serving a different theology. Chartres, Notre-Dame and York Minster all resolve into a ring count and a spoke count, and reading a rose window is largely a matter of finding those two numbers and then seeing what the tracery does between them.

Islamic geometric ornament uses the radial grid as the starting framework for its star patterns: a circle, a division into some number of parts, and then a construction that connects those divisions to produce the star. Most of the famous patterns can be traced back to a spoke count and a rule for joining points.

Compass roses, ships' wheels, clock faces, wheel-thrown pottery decoration, Celtic and Norse circular ornament, Native American medicine wheels, Chinese ceiling caissons, Byzantine floor mosaic — all radial constructions, and all describable by the same two numbers.

For contemporary work the grid does the same job it always did. Logo marks with rotational symmetry need to close exactly, and the eye is unforgiving about a mark that is nearly but not quite symmetrical. Data visualisations in polar coordinates need their divisions to be honest. Pottery and woodturning decoration needs to divide the circumference correctly.

Laying the grid over an existing image is the fastest way to read a radial design you want to copy. Load a photograph of the rose window, adjust the spoke count until the divisions line up with the tracery, and you have the fold. It is almost always faster than counting the elements by eye, which is error-prone once the count goes above about eight.

For a measured spiral rather than an ornament, the polar grid generator adds the ruled rings, and the Sri Yantra generator draws one specific radial figure exactly. To draw the figure itself rather than lay a guide over your own work, the mandala generator repeats each stroke around the centre as you make it. For drawing, the sequence is centre outward, always. Every ring has to accommodate what is inside it, and a mandala planned from the outside in tends to run out of room somewhere around the third band. That is not a rule of art; it is a consequence of the area relationship.

A common mistake is choosing the ring count first. The rings are subordinate — they divide up the space the spokes have already made — so setting them before the symmetry is decided means adjusting them again once it is.

Another is using a very high spoke count for a small drawing. Thirty-six spokes on a hand-sized mandala puts the outer divisions less than a centimetre apart at the rim and much closer than that further in, which is finer than most media can hold.

The grid draws over your image rather than exporting a fixed template because the placement of the centre is a compositional decision. A mandala centred in the frame reads as formal; one placed off-centre reads as a subject within a picture rather than as the picture itself.

Export sizes itself from the paper format and the DPI you choose rather than from your screen, so an A3 sheet at 600 DPI has genuinely fine construction lines. SVG keeps every ring and spoke as an editable path, which is what you want when the grid is scaffolding you will delete.

Everything runs in your browser. Images you load are never uploaded, because there is no server for them to reach. The drawing, the transform and the export all happen on your own machine.