PS
# venus.m4
# https://tex.stackexchange.com/questions/576423/a-more-precise-dance-of-planets-with-metapost-and-tikz
# https://tex.stackexchange.com/questions/575986/dance-of-venus-and-variations-in-tikz-pgf

gen_init
NeedDpicTools
maxpsht = 20

thinlines_

define(`venus',
`setkeys_(`$1',
 outerlength:4;
 innerlength:2.8933;
 outerrate:8;
 innerrate:13;
 maxtimes:2880;
 increment:2;
 changephase:0 )
 sizefactor = 165/200
 nmaxtimes = 360*m4outerrate
 for x=0 to nmaxtimes by m4increment do {
   if "$2" != "" then { hue = \
       abs(sind(360*x/nmaxtimes*abs(m4innerrate-m4outerrate)+m4changephase-60))
     hsvtorgb(hue*360,1,1,r,g,b)
     line from (Rect_(m4outerlength,x))*sizefactor \
       to (Rect_(m4innerlength,x/m4outerrate*m4innerrate))*sizefactor \
       outlined rgbstring(r,g,b) } \
   else {
     line from (Rect_(m4outerlength,x))*sizefactor \
       to (Rect_(m4innerlength,x/m4outerrate*m4innerrate))*sizefactor
     }
   } ')

AA:[
 sizefactor = 1/2.54
 define(`venusA',`[
 setkeys_(`$1',
   iterations:270;
   outerdistance:5.41;
   innerdistance:7.48;
   outerperiod:123;
   innerperiod:200;
   step:5)
   for x=0 to m4iterations by m4step do {
     line from (Rect_(m4outerdistance,x))*sizefactor \
       to (Rect_(m4innerdistance,x/m4outerperiod*m4innerperiod))*sizefactor \
       outlined "gray"
     }
   ]')

# 3 columns, 5 rows
 sizefactor /= 3
 Orig:(0,0)
 for i=1 to 5 do {
   iteri = 180 + (i-1)*540
   for j=1 to 3 do {
     if (i==1) && (j==1) then { iter = 270 } \
     else { iter = iteri + (j-1)*180 }
     V[i,j]: venusA(iterations=iter) with .sw at Orig
     sprintf("%g",iter) at last [] #colored rgbstring(1,0,0)
     Orig: V[i,j].se
     }
   Orig: V[i,1].sw-(0,V[i,1].ht)
   }
 ]

BB:[
 venus(outerrate=8;innerrate=17;increment=2;innerlength=3.5;changephase=60,T)
 ] at AA
# ] with .nw at AA.sw+(0,-0.5)

PE