Definition. Let $\varepsilon \in (0;1)$. The $\varepsilon$-snowflake of a metric space $(X,d)$ is the metric space $(X,d^\varepsilon)$, with the induced metric $d^\varepsilon(a,b) := d(a,b)^\varepsilon$ for all $a,b \in X$.
Consider the unit interval $X = [0;1]$ for $\varepsilon = \frac{1}{2}$ with the standard metric $$ d: X \times X \to \mathbb{R}_+, \\ (a,b) \mapsto d(a,b) := |a-b|. $$ Then, $(X,d^\varepsilon)$ is a snowflake with the metric $d^\varepsilon(a,b) = |a-b|^\frac{1}{2}$.
My question: Is there a way to visualize $(X,d^\varepsilon)$ in this example? (like something you could draw on a blackboard...)
