How to scale Phase Transition Diagram for Compressed Sensing?
I recommend first fixing $N$. By the way, remember here that compressed sensing works asymptotically well; for $N \rightarrow \infty$ your phase transition is going to move up/left (better) in the $\delta, \rho$ diagram, see for example Donoho &amp; Tannner 2010.

Your size of $N$ essentially determines the resolution you can achieve in your phase transition diagram. For example we can look at Maleki &amp; Donoho 2010, Section IV: they describe how they select $N = 800$ and then calculate $n$ and $k$ from a grid of values $(\delta, \rho)$ between 0.05 and 1 in 30 steps. For each value $\delta$ or $\rho$, the corresponding $n$ or $k$ are calculated as $$n = \lceil \delta N\rceil,$$ respectively $$k = \lceil \rho n \rceil.$$

As you can see there is generally some imprecision involved during to the rounding. If you select a too fine grid of values $(\delta, \rho)$ for a given $N$, several of the resulting $n$ or $k$ values are going to round to the same number. You will have to either select a larger $N$ or choose a coarser grid for your $(\delta, \rho)$ to avoid this.

Finally, you should (if you want the same type of plot as Donoho et al.) plot your success ratio in each of your points in a $(\delta, \rho)$ coordinate system. Your figure above looks as if it was perhaps plotted with $k$ on the first axis?

Now, if you wish to estimate the actual phase transition boundary, you can also see in Maleki &amp; Donoho 2010, Section IV, how they fit a logistic curve to the success ratios and can then read a specific percentage reconstruction boundary $\rho$ for each value $\delta$ from the fitted logistic function.