Abstract: In this paper，a subdivision-and-adding scheme of constructing fractal curves from Bezier-curves is created.First，we gain subdivided curve sequence by subdividding parameter-2-perioded Bezier curves recursively，then we add these subdivided curve sequence in file infinitely，by this means，we construct continuous and non-differentiable fractal curves，these curves have the property of self-similitude.The Bezier fractal curve can be indicated as linear combination of control-vertex of the original Bezier curve，the mixed function is created by adding parameter-2-perioded Bernstein basis function infinitely，it has the properties of continuity and non-differentiable and self-similitude.Numerical experiments indicate that curves created by this subdivision-and-adding scheme have fractal character.

Key words: Bezier curve, subdivision-and-adding, fractal

摘要： 给出了一种由Bezier曲线生成分形曲线的细分叠加方法。将参数二周期化后的Bezier曲线进行递归细分，得到细分曲线序列，再依次将此细分曲线序列无限叠加，构造出处处连续而处处不可微的分形曲线，具有某种自相似性。此Bezier分形曲线可表示为原Bezier曲线控制顶点的线性组合，其调配函数由参数二周期化后的Bernstein基函数无限细分叠加生成，处处连续而处处不可微，且有某种自相似性。数值实验表明此细分叠加方法所生成的曲线具有分形特征。

关键词: Bezier曲线, 细分叠加, 分形