Generate a modulo rosace
Mathematica, 192 bytes

This type of challenge (nontrivial mathematical computation together with high-level graphics output) is what Mathematica is made for!

(d=#;r_~t~n_:=r{Sin[#],Cos[#]}&amp;[6.3n/d];m=Mod[10#,d]&amp;;Graphics@{Array[#~Text~t[9,#]&amp;,d,0],Array[Arrow@{t[9,#+1/7],t[9,#+6/7]}&amp;,d],Array[Arrow@BezierCurve@{t[8,#+1/9],{0,0},t[8,m@#-1/9]}&amp;,d]})&amp;


Expanded and explained:

[1] (
[2] d = #; r_~t~n_ := r {Sin[#], Cos[#]} &amp;[6.3 n/d]; m = Mod[10 #, d] &amp;;
[3] Graphics@{
[4]   Array[#~Text~t[9, #] &amp;, d, 0],
[5]   Array[Arrow@{t[9, # + 1/7], t[9, # + 6/7]} &amp;, d],
[6]   Array[Arrow@BezierCurve@{t[8, # + 1/9], {0, 0}, t[8, m@# - 1/9]} &amp;, d]
[7]          }
[8] ) &amp;


Lines 1 and 8 delimit an unnamed function of one argument. Lines 3 and 7 delimit several commands that output graphics.

Lines 2 stores the input as d; defines a binary function t giving the coordinates of a point n/d of the way around the circle of radius r, clockwise from the top (in the spirit of this site, I saved a byte by rounding 2π to 6.3!); and defines a unary function m calculating the destination of the arrow starting at its argument.

Line 4 renders the numbers 0 to d–1 equally spaced around the circle of radius 9 (the exact radius unimportant, chosen to maximize aesthetics subject to fitting in one byte).

Line 5 renders the clockwise straight arrows around the circumference of the circle. The 1/7 and 6/7 leave enough space to read the numbers.

Line 6 renders the curved arrows from each number to (10 times the number modulo d). BezierCurve automatically draws a Bézier curve using the given control points. Fortunately, using the origin as a single interior control point produces reasonable output.

Sample output (note that the cases 9, 10, and 11 are trivial in different ways):

d = 7



d = 8



d = 9



d = 10



d = 11



d = 12



d = 13



d = 37



This last input was chosen because 37 divides 10^3–1, and so the interior arrows (not counting the obligatory self-arrow from 0 to 0) form lots of triangular cycles.