Self-similar figures (such as fractals) primarily exhibit scale symmetry ((also called dilation symmetry or scaling symmetry), which is a type of similarity symmetry. Here’s a detailed elaboration: --- 1. What scale symmetry means In scale symmetry, an object looks the same (or statistically the same) when magnified or shrunk by certain factors. Mathematically, if you scale the figure by a factor \( r \), the result is congruent or similar to the original — but unlike translational or rotational symmetry, the “copy” is a different size. --- 2. Discrete vs. continuous scale symmetry - **Discrete scale symmetry**: Invariant under scaling by specific factors only (e.g., the Sierpiński triangle is invariant under scaling by factor \( \frac{1}{2} \), meaning if you zoom in by factor 2 on certain points, you see the same pattern). - Continuous scale symmetry: Invariant under scaling by any factor (e.g., a perfect straight line or a logarithmic s...