Figure 2.

Fractal dimensions for polymers to characterize the effective conformational states. For example, $d_{\text{f}}=1$ and 3 correspond to a straight line and the most compact state, respectively. The polymer with the excluded volume effect forms an extended state with $d_{\text{f}}\cong 5/3$. For $d_{\text{f}}=2$, the ideal chain is a polymer corresponding to a random-walk conformation.