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snowflake

于 2012-05-13 发布文件大小:1KB

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对一个等边三角形，每条边按照Koch曲线的方式进行迭代，产生的分形图称为Koch雪花。编制程序绘制出它的图形，并计算Koch雪花的面积，以及它的分形维数(An equilateral triangle, each edge iterations, in accordance with the manner of the Koch curve generated fractal images is known as the Koch snowflake. Programmed to draw its graphics, and calculate the area of the Koch snowflake, and its fractal dimension)

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ForcedPendulum
This simulink model simulates the damped driven pendulum, showing it s chaotic motion. theta = angle of pendulum omega = (d/dt)theta = angular velocity Gamma(t) = gcos(phi) = Force omega_d = (d/dt) phi Gamma(t) = (d/dt)omega + omega/Q + sin(theta) Play with the initial conditions (omega_0, theta_0, phi_0 = omega(t=0), theta(t=0), phi(t=0)) and the system parameters (g, Q, omega_d) and the solver parameters/method. Chaos can be seen for Q=2, omega_d=w/3. The program outputs to Matlab time, theta(time) & omega(time). Plot the phase space via: plot(mod(theta+pi, 2*pi)-pi, omega, . ) Plot the Poincare sections using: t_P = (0:2*pi/omega_d:max(time)) plot(mod(spline(time, theta+pi, t_P), 2*pi)-pi, spline(time, omega, t_P), . ) System is described in: "Fractal basin boundaries and intermittency in the driven damped pendulum" E. G. Gwinn and R. M. Westervelt PRA 33(6):4143 (1986) (This simulink model simulates the damped driven pendulum, showing it s chaotic motion. theta = angle of pendulum omega = (d/dt)theta = angular velocity Gamma(t) = gcos(phi) = Force omega_d = (d/dt) phi Gamma(t) = (d/dt)omega+ omega/Q+ sin(theta) Play with the initial conditions (omega_0, theta_0, phi_0 = omega(t=0), theta(t=0), phi(t=0)) and the system parameters (g, Q, omega_d) and the solver parameters/method. Chaos can be seen for Q=2, omega_d=w/3. The program outputs to Matlab time, theta(time) & omega(time). Plot the phase space via: plot(mod(theta+pi, 2*pi)-pi, omega, . ) Plot the Poincare sections using: t_P = (0:2*pi/omega_d:max(time)) plot(mod(spline(time, theta+pi, t_P), 2*pi)-pi, spline(time, omega, t_P), . ) System is described in: "Fractal basin boundaries and intermittency in the driven damped pendulum" E. G. Gwinn and R. M. Westervelt PRA 33(6):4143 (1986) )

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