Analemma is the path the sun follows in the sky for a given time all through the year.
It is caused due to the inclination of the orbit and eccentricity of the orbit of the planet
The x axis is the equation of time and y axis is declination of the sun.
Change different parameters to see how they affect the shape of analemma.
e = eccentricity of the orbit. How much the orbit of the planet is deviating from circular
ε = inclination of the axis of the planet
φ = difference in days from perihelion (nearest point on orbit) and winter solstice. This is like a phase difference between the cycle of declination change and the angular position of planet on elliptic orbit.
There are deformations for extreme values of orbital eccentricity and tilts due to approximations in calculations