Equation collage

Is it possible to make an equation collage using all the equations within a document?

So far I have exported all the equations with

\documentclass{article}
\usepackage{amsmath}
\usepackage[active,tightpage,displaymath]{preview}
\makeatletter
\renewcommand\tagform@[1]{}
\makeatother

\begin{document}

$$x^2+2x+1=0$$

$$F=\int dx~f(x)$$

\end{document}


to output a file with all the equations without numbering. Then used

pdfcrop output.pdf


to crop them. However I'm not sure how to proceed next, in order to generate the collage automatically. I have three options:

1. scale each image randomly and then stack them, trying to minimize empty space between the equations. Something like this https://www.kn3.net/ana_caro/35-3-3-6-4-7-3-4-363-JPG.html

2. assign random opacity to each equation and overlap them like https://media.gettyimages.com/vectors/quantum-physics-formulas-over-blackboard-vector-id500260145

3. rotate all images at a angle and have them overlap, creating a background like this https://media.gettyimages.com/vectors/math-background-vector-id165979446

• It is an interesting question. But it would definitely be helpful for you to provide a full MWE, and not just code fragments. – Steven B. Segletes May 14 '18 at 9:56
• @StevenB.Segletes done. – Prastt May 14 '18 at 10:12