The ‘Devils Staircase’ is a famous function in mathematics. It is a non-constant function that has $0$ derivative almost everywhere. Further it is continuous but not absolutely continuous. Constructing the devils staircase is easy, and is done recursively. We start with the function $f_0:[0,1]\to [0,1]$ where $f_0(x)=x$. Now suppose we have defined $f_n$ we define $f_{n+1}$ by letting it be $1/2$ on the interval $[1/3,2/3]$, then we take a copy of the full function $f_n$ and “squash” it into the box with vertices : $(0,0),(1/3,0),(1/3,1/2),(0,1/2)$, then again we take a copy of $f_n$ and we “squash” it into the box with...