Newton's method for f(z)=z sin A pi (z+i) sin A pi (z-i)

Buttons, fields and how to use with the applet.

• z= A field to enter a complex number, the first place is for the real part, the second one for the imaginary part.
• Limes: Calculate the limit of N^k(z) where z ist as given by the user (z=) and k runs to infinity. The result is shown in the center of the top line.
• A: set the variable (default is 1) to the value given after z= and redraw the picture.
• Iterations: Enter the number of iterations (default is 100) which are used to detect convergence. Then press Draw! Reduce the number of iterations to speed up the applet.
• Draw! Redraw the picture. Please be patient with this applet, it might take a while.
• Coordinates: Move the mouse pointer over the applet, and you are given the complex coordinates (real part | imaginary part) of it.
• +/-: Zoom in (+) or out (-). Be patient, the calculations are not very fast.
• Click inside the picture to change the given part of the complex plane. Sorry, this part seems not to work appropriately.

Legend

white: undefined numbers occur in calculation

black to deep blue: infinity or too large numbers occur. The color depends on the number of iterations until when this happens.

grey to blue, dark: no convergence detected.

rest: convergence to a zero of f. The colors are chosen depending on the zero and the brightness reflects the number of iterations until convergence was detected.