Figure 2.

A linear-log plot of the bricklayer’s graphs’ robustness ${\rho }_p^{\max }$ for n vertices, given by equation (3.6), versus frequency (number of vertices n divided by k^ℓ), where ℓ = 6 and k = 2. Each blue dot denotes a possible neutral set size. The green line denotes the continuous everywhere but differentiable nowhere ‘blancmange-like curve’ (here k = 2, so one component of this line is exactly equivalent to the Tagaki curve [50]) that is given by the continuous n_p version of equation (3.6), corresponding to ${\rho }_{\hspace{0.17em}p}^{\max }$. The upper and lower bounds on ${\rho }_{\hspace{0.17em}p}^{\max }$, given by equation (3.8), are also plotted. The upper bound is equivalent to the simple form ρ_p = ℓ⁻¹log_k n_p = 1 + log_k(f_p)/ℓ. Plots like this, containing the exact maximum robustness as well as the upper and lower bounds, can be generated with our free, open-source web tool RoBound Calculator [52].