Gravitational lensing can be by a faint star , a trillion stars of a galaxy , or a cluster of galaxies , and this poses a familiar struggle between particle method and mean field method .
In a bottom-up approach , a puzzle has been laid on whether a quadruple lens can produce 17 images .
The number of images is governed by the gravitational lens equation , and the equation for n -tuple lenses suggests that the maximum number of images of a point source potentially increases as n ^ { 2 } +1 .
Indeed , the classes of n = 1 , 2 , 3 lenses produce up to n ^ { 2 } +1 = 2 , 5 , 10 images .
We discuss the n -point lens system as a two-dimensional harmonic flow of an inviscid fluid , count the caustics topologically , recognize the significance of the limit points and discuss the notion of image domains .
We conjecture that the total number of positive images is bounded by the number of finite limit points 2 ( n - 1 ) :n > 1 ( 1 limit point at \infty if n = 1 ) .
A corollary is that the total number of images of a point source produced by an n -tuple lens can not exceed 5 ( n - 1 ) :n > 1 .
We construct quadruple lenses with distinct finite limit points that can produce up to 15 images and argue why there can not be more than 15 images .
We show that the maximum number of images is bounded from below by 3 ( n + 1 ) :n \geq 3 .
We also comment on “ thick Einstein rings ” that can have one or more holes .