page_title: Complex quadratic polynomial
section_title: Critical curves
hierarchical_section_title: Complex quadratic polynomial / Critical items / Critical curves
caption_attribution_description: English: This picture is derived from File:LogisticMap BifurcationDiagram.png by PAR. It shows the first iterates x n + 1 = r x n ( 1 &#x2212; x n ) {\displaystyle x_{n+1}=rx_{n}(1-x_{n})\,} for x = 0.5 and n=0,... 5, while leaving the original attractor slightly visible in the background. At x=0.5, the derivative of the logistic function vanishes, which is what "attracts" non-periodic points, thereby producing the typical shadows the attractor features.
context_page_description: A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers.
context_section_description: Diagrams of critical polynomials are called critical curves.
  These curves create the skeleton (the dark lines) of a bifurcation diagram.
caption: Critical curves
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