Consider the Mandelbrot sequence with seed s = -0.75. Show that this Mandelbrot sequence

Chapter 12, Problem 58

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QUESTION:

Consider the Mandelbrot sequence with seed s = -0.75. Show that this Mandelbrot sequence is attracted to the value -0.5. (Hint: Consider the quadratic equation x2 - 0.75 = x, and consider why solving this equation helps.)

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QUESTION:

Consider the Mandelbrot sequence with seed s = -0.75. Show that this Mandelbrot sequence is attracted to the value -0.5. (Hint: Consider the quadratic equation x2 - 0.75 = x, and consider why solving this equation helps.)

ANSWER:

Step 1 of 2

Let us consider the Mandelbrot sequence with seed .

To prove that this Mandelbrot sequence is attracted to the value -0.5.

Given seed is . Then, the recurrence relation for the Mandelbrot sequence is

                             (i)

Suppose for sufficiently large , approaches to some value .

Then, from equation (i),

                                               (ii)

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