k = n / d;
* Changes a lot, from different 'k' values, to complete a drawing!
Rect. plot 'x' size cosine freq.
Rect. plot 'y' size sine freq.
Rect. plot 'x' size.
Rect. plot 'y' size.
x freq.: 6 | y freq.: 8 | x size: 0.33 | y size: 0.33
Frames goes to 'zero', which triggers a canvas reset check.
CLICK ON BUTTONS TO CHANGE INPUTS!!!
* You can save a frame by right-clicking the canvas, however, good luck picking a good plot.
* By increasing "Seconds", you can lower the plot pixel distance.
* Use the chart above to pick a rose. Each rose have a perimeter, so change the final angle with "Turns" input.
NON-ZERO INTEGER 'k':
* The curve will be rose-shaped with '2k' petals if 'k' is even, and 'k' petals when 'k' is odd.
* Each peak corresponds to a point lying on the circle 'r=a'. Line segments connecting successive peaks will form a regular polygon with an even number of vertices that has its center at the pole and a radius through each peak.
ROSES WITH RATIONAL NUMBER VALUES FOR 'k':
* When both 'n' and 'd' are odd, the positive and negative half-cycles of the sinusoid are coincident. The graph of these roses are completed in any continuous interval of polar angles that is 'pi' long.
* When 'n' is even and 'd' is odd, or visa versa, the rose will be completely graphed in a continuous polar angle interval '2 * d * PI' long. Furthermore, the roses are symmetric about the pole for both cosine and sine specifications.
* In addition, when 'n' is odd and 'd' is even, roses specified by the cosine and sine polar equations with the same values of 'a' and 'k' are coincident. For such a pair of roses, the rose with the sine function specification is coincident with the crest of the rose with the cosine specification at on the polar axis either at 'theta = d * pi / 2' or at 'theta = 3d * pi / 2'. This means that roses 'r = a * cos(k * theta)' and 'r = a * sin(k * theta)' with non-zero integer values of 'k' are never coincident.
A rose curve specified with an irrational number for 'k' has an infinite number of petals and will never complete!