Length contraction gives $L' = \frac{L}{\gamma}$. Say the system $S'$ moves at a certain velocity $v_0\hat{x}$, and lets look at the distance between two points:$$d=\mid p_1 - p_2 \mid$$ $$d' = \mid \frac{p_1}{\gamma} - \frac{p_2}{\gamma}\mid =\mid \frac{p_1-p_2}{\gamma}\mid$$ So the relation between two points can't switch with regards to the origin $O'$, if $p_1$ is closer than $p_2$ to the origin it'll remain this way. That is because $\gamma=\frac{1}{(1-v^2/c^2)^{0.5}}>0$. So my understanding is that objects won't change the number of "holes"/"gaps" they have, and will only contract. The equation for contraction of a parameterized circle for example with regards to $x$ is: $$x=rcos(\theta), y = rsin(\theta)\rightarrow x'=\frac{ rcos(\theta)}{\gamma},y = rsin(\theta)$$ or with an equation (note the differences in the "contraction term"): $$x^2+y^2=r\rightarrow (\gamma x)^2+y^2=r$$

Length contraction gives $L' = \frac{L}{\gamma}$. Say the system $S'$ moves at a certain velocity $v_0\hat{x}$, and lets look at the distance between two points:$$d=\left| p_1 - p_2 \right|$$ $$d' = \left|\frac{p_1}{\gamma} - \frac{p_2}{\gamma}\right|=\left| \frac{p_1-p_2}{\gamma}\right|$$ So the relation between two points can't switch with regards to the origin $O'$, if $p_1$ is closer than $p_2$ to the origin it'll remain this way. That is because $\gamma=\frac{1}{\sqrt{1-v^2/c^2}}>0$. So my understanding is that objects won't change the number of "holes"/"gaps" they have, and will only contract. The equation for contraction of a parameterized circle for example with regards to $x$ is: $$x=r\cos(\theta), \quad y = r\sin(\theta)\longrightarrow x'=\frac{ r\cos(\theta)}{\gamma}, \quad y = r\sin(\theta)$$ or with an equation (note the differences in the "contraction term"): $$x^2+y^2=r\rightarrow (\gamma x)^2+y^2=r$$