page_title: Misiurewicz point
section_title: Branch points
hierarchical_section_title: Misiurewicz point / Quadratic maps / Examples of Misiurewicz points of  complex quadratic mapping / Branch points
caption_attribution_description: Three external rays ( 9, 11 and 15 /56) landing on the main Misiurewicz point of 1/3 limb of mandelbrot set. image made with Mandel - program for DOS by Wolf Jung, version 3.5 see: http://www.iram.rwth-aachen.de/~jung/indexp.html It is probably mathemathically most advanced program for drawing mandel / Fatou / Julia sets Commands: 1&lt; enter &gt;&#160;; q = 2&#160;; e = 0/1 &lt; enter &gt;&#160;; F9&#160;; &lt; end &gt;
context_page_description: In mathematics, a Misiurewicz point is a parameter in the Mandelbrot set for which the critical point is strictly preperiodic. By analogy, the term Misiurewicz point is also used for parameters in a multibrot set where the unique critical point is strictly preperiodic.
context_section_description: Point  
  is a principal Misiurewicz point of the 1/3 limb
  it has 3 external rays:  9/56, 11/56 and 15/56.
caption: c
          =
          
            M
            
              4
              ,
              1
            
          
        
      
      {\displaystyle c=M_{4,1}}
exif: {}