The ratio of the periods of the Earth and Venus orbits is extremely close to a low integer rational number ratio which leads to a nearly periodic earthcentric orbit, that is, the orbit of Venus relative to the Earth as the center of the polar coordinates in the plane of their common orbit, not rotating with respect to the "fixed stars". The idea for this Maple plot comes from the little book "A Little Book of Coincidence" by John Martineau [Amazon, Facebook, website].
The fact that their almost common period is not exact leads to a slow precession of the orbit visible in the thickening of the orbit during its second cycle.