For a logarithmic spiral, rotating through a fixed angle multiplies the radius by a fixed factor. The angle between the tangent and radius stays constant, expressing the same self-similarity at every scale.对数螺线每转过一个固定角度，半径就乘以同一个比例因子。切线与半径的夹角保持不变，因此不同尺度下保留相同的形态。
The point moves outward on . The highlighted radius grows exponentially; each full turn multiplies its length by .光点沿 向外移动，高亮半径按指数增长。每转一整圈，长度就乘以 。