Initially I mistakenly coded the drawer in a way that the rotational directions of the inner circle and the dots are inconsistent. My original mistake made the "petals" pointing inward. I fixed this bug on Feb. 21st, but I keep an option that can replicate my previous mistake.

Normal direction	Reverse direction

Dot distance affects how broad the pattern is.

Short distance	Long distance

Dot rotation affects the angular distance between curves

Blue dot rotation: 150° Green dot rotation: 115°	Blue dot rotation: 150° Green dot rotation: 150°

The size of the inner circle radius relative to the outer circle radius can significantly affect the pattern. Their greatest common divisor determines the density of the curves drawn. The following graphs were drawn using the same outer circle radius (the default value -- 300).

Radius: 120, gcd: 60	Radius: 105, gcd: 15	Radius: 110, gcd: 10

Mathematically, if r_o is the outer circle radius, r_i is the inner circle radius, and R is the radians which the inner circle must rotate through to complete the curve, then R can be found using the following formula

where gcd means the greatest common divisor.

This implies that the greater the greatest common factor between the outer and inner circle radius, the shorter the path which the inner circle will rotate through will be.

Besides, you can enter either a positive or a negative number for the inner circle radius parameter. If it's positive, then the final pattern produced will be a hypotrochoid, otherwise an epitrochoid will be drawn. The following graphs were drawn using 140 as the outer circle radius.

Inner circle radius: 60 Drawing direction: normal	Inner circle radius: -60 Drawing direction: normal

Inner circle radius: 60 Drawing direction: reversed	Inner circle radius: -60 Drawing direction: reversed

When the gcd between the outer and inner circle radius is small, the drawing may become complicated and less clear (the left figure). In such cases, you may consider to reduce the "completeness" parameter.

Completeness: 1	Completeness: 0.114

Drawing step affects the quality of the drawing. The smaller the step, the better the quality of the drawing will be, but the cost is the drawing time. Normally, the default drawing step (0.005) is sufficient. If you find that lines become dotted, then you should consider to reduce this parameter.

Try to reduce step	Good