Forms
When the quadratic polynomial has only one variable ( univariate ), one can distinguish its 4 main forms:
- The general form : where .
- The factored form used for logistic map
- which has an indifferent fixed point with multiplier at the origin
- The monic and centered form,
The monic and centered form has the following properties:
- It is the simplest form of a nonlinear function with one coefficient (parameter),
- It is an unicritical polynomial, i.e. it has one critical point,
- It is a centered polynomial (the sum of its critical points is zero),
- It can be postcritically finite, i.e. If the orbit of the critical point is finite. It is when critical point is periodic or preperiodic.
- It is a unimodal function,
- It is a rational function,
- It is an entire function.
Read more about this topic: Complex Quadratic Polynomial
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“The necessary has never been man’s top priority. The passionate pursuit of the nonessential and the extravagant is one of the chief traits of human uniqueness. Unlike other forms of life, man’s greatest exertions are made in the pursuit not of necessities but of superfluities.”
—Eric Hoffer (1902–1983)