Complex Analysis: Theory and Applications · Problem 4.2.8

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · mandelbrot-set-real-cusp

Problem

Show that, if

c

is any real number greater than

\dfrac{1}{4}

, then

c

is not in the Mandelbrot set. Note: Combining this condition with Example 4.11 shows that the cusp in the cardioid section of the Mandelbrot set occurs precisely at

c = \dfrac{1}{4}

Related theory

Real Numbers And The Real Line

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