Rose Curve Generator

How the Rose Curve Generator works

Rose curve generator: getting a good result

In polar coordinates a point is described by its distance r from the centre and its angle θ. The rose curve says the distance swings between 1 and −1 as a cosine of k times the angle, and a negative distance means the point is plotted on the opposite side. That folding is why an odd k gives k petals but an even k gives 2k: with even k the negative lobes land between the positive ones instead of on top of them.

Choosing k. The sliders set k = n ÷ d, reduced to lowest terms. With d = 1 you get the simple flowers: k = 1 is a circle, 2 is a four-leaf clover, 3 a three-petal, 4 an eight-petal, 5 a five-petal. With d greater than 1 the curve takes several turns to close and the petals overlap. k = 2/3 is a three-lobed loop, 5/3 a five-pointed star with curved sides, 7/4 a dense fourteen-petal rosette. The stats line reports the reduced k and the petal count.

Layers draws the same curve several times, each smaller and rotated by a fraction of a petal, so the copies nest inside one another. With Filled and a low alpha, the overlaps build into a layered paper-cut look; with Outline they read as a mandala. A single layer is the plain mathematical figure.

Colour. Rainbow gives each layer its own hue; Single uses one hue from the seed, and Regenerate only rotates the hue because the shape is set entirely by the sliders.

Export. The curve is scaled to the shorter side of the export, so it is complete and centred at any size. A square 2048 × 2048 export suits a print or an avatar; a widescreen 3840 × 2160 leaves ground colour either side of the flower, which reads well as a desktop wallpaper with icons on the left. Nothing is upscaled: the curve is recomputed from the sliders at the new size and every petal edge stays sharp.

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