What is the joke that is shown in this picture?
As commented by @long, the elements shown are not completely randomised. The elements in all the rows, except in the 3rd row ($\ce{Na, K, Ca}$), are arranged in same order as they are given in periodic table.

After studying them on periodic table for 15 minutes, it seemed to have no meaning. There are no periodic trends. $\ce{H, Li, Na, K, Rb}$ belongs to IA group, $\ce{Be, Ca, Sr}$ belongs to IIA group. And they are arranged in a random way, having no meaning.

The picture is clearly a joke showing that when scientist have eye check-up, they have to read elements instead of alphabets.