21.2 images2.input

These images illustrate how Newton’s method converges when computing the Newton iteration complex cube roots of 2. Each point in the (x,y)-plane represents the complex number x+iy, which is given as a starting point for Newton’s method. The poles in these images represent bad starting values. The flat areas are the regions of convergence to the three roots.

)read newton                                       Read the programs from
)read vectors                                      Chapter 10
f := newtonStep(x^3 - 2)                          Create a Newton’s iteration
function for x3=2

The function fn computes n steps of Newton’s method.

clipValue := 4                                     Clip values with magnitude > 4

drawComplexVectorField(f^3, -3..3, -3..3)         The vector field for f3
drawComplex(f^3, -3..3, -3..3)                    The surface for f3 drawComplex(f^4, -3..3, -3..3)                    The surface for f4