中文摘要：

运用Weierstrass-Mandelbrot函数构建了钛基氧化物电极（Ti／MO2）的分形表面，采用Monte Carlo方法对电极的伏安曲线进行了模拟，主要考察了扫描速率和分形维数对伏安曲线的影响。结果表明：在分形维数一定的情况下，随着扫描速率的不同，峰电势不发生变化，峰电流与扫描速率的平方根呈线性关系；随着分形维数的增大，峰电流增大，电极的电催化性能增强。模拟结果与理论一致。分形维数与Monte Carlo模拟的结合可为钛基氧化物电极的深入研究提供一种新思路。

英文摘要：

A fractal surface of titanium based oxide electrode （Ti/MO2） was constructed by Weierstrass-Mandelbrot function, and voltammogram on electrode were simulated by Monte Carlo method. The effects of scan rate and fractal dimension on voltammogram were mainly studied. The results indicated that at fixed dimension, the positions of peak potential on fractal electrodes don＇t alter at different scan rates; the peak currents are proportional to the square root of the scan rate; the peak current and catalytic activity of anode increase with the increasing of fractal dimension of electrode. The simulation results coincide well with theory. The combination of fractal theory and Monte Carlo simulation can provide a new method for studying titanium based electrodes.