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Consider the Mandelbrot sequence with seed s = -0.75. Show that this Mandelbrot sequence
Chapter 12, Problem 58(choose chapter or problem)
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.)
Questions & Answers
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)