# Contours with equal area changing system

Let’s say I have a system with 3 particles in 2d system a,b,c with the following positions

a = [0.1,0.0]
b = [-0.1,0.0]
c = [0.0,0.1]


each particle is described by Gaussian function, therefore the system function is as followed:

σ = 0.08
f(x,y) = exp(-((x-a)^2+(y-a)^2)/(2(σ^2)))+exp(-((x-b)^2+(y-b)^2)/(2(σ^2)))+exp(-((x-c)^2+(y-c)^2)/(2(σ^2)))


I draw the initial system shape

x = range(-0.5,stop=0.5,length=50)
y = range(-0.5,stop=0.5,length=50)
contour(x,y,f,levels=[1.0],aspect_ratio=:equal) using Plots package. After a while the particles move to other positions,for instance:

a = [0.1,-0.05]
b = [-0.1,0.0]
c = [0.05,0.1]


which changes the shape of the contour according to the same f(x,y) function (with the same sigma). I need to produce a closed contour that keep the same area for the new particle positions. How do I do that? or How can I find the “level” to reach the same area? This was an example, in fact I have many particles in my function. The Domain Astro/Space might also able to contribute

in “level” I mean to levels=[1.0] inside the contour command. In this example, initially it would be 1.0, what would be the next value after the system evolvement?