Skip to main content
Home
luz

Main navigation

  • Home
  • research
  • scators
  • optics
  • ciencia
  • arsciencia

Breadcrumb

  1. Home
  2. scators

fractals

Profile picture for user mfg
By mfg, 7 November, 2017

The quadratic mapping can be performed with hypercomplex scator numbers in $1+n$ dimensions.

 

ix set
conjunto ix  c2i0E-1+2(-.67;.007,-.25)(-1.91;-.002,.3)

Notation used to label visualizations:

\[ \underset{\textrm{confined quadratic iteration}}{\underbrace{c2i}}\overset{\textrm{parameter/dynamical space}}{\overbrace{0/\left(s_{i};x_{i},y_{i}\right)}}\underset{\textrm{algebra and dimension}}{\underbrace{\mathbb{S}_{\pm}^{1+2}}}\overset{\textrm{fractal location}}{\overbrace{\left(s;x,y\right)}}\underset{\textrm{viewpoint}}{\underbrace{\left(p_{0};p_{1},p_{2}\right)}} \]

  • $\textbf{c2i}$  $\textbf{c}$onfined $\left\{ \boldsymbol{2}\right\} $quadratic $\textbf{i}$terations, (that can be generalized to $\textbf{cpi}$ for a pth power polynomial or p$\rightarrow \textbf{func}$ for other $\textbf{func}$tion's mappings)
  • followed by $\textbf{0}$ if the initial value of the variable is set to zero (set depicted in parameter space) or the initial value $\left(s_{i};x_{i},y_{i}\right)$ at which the constant is fixed (set depicted in dynamical space)
  • followed by the number system: $\mathbb{R}$ real, $\mathbb{C}$ complex, $\mathbb{H}$ hyperbolic, $\mathbb{S}_{-}^{1+n}$  imaginary scators or $\mathbb{S}_{+}^{1+n}$  real scators (in $1+n$ dimensions), etc.
  • followed by the fractal location or plane in 2D $\left(s;x,y\right)$ that is being depicted.
  • followed, if necessary, by the viewpoint $\left(p_{0};p_{1},p_{2}\right)$.
  • in 3D renderings, fractal location and viewpoint are stated.

There are two distinct fractal family sets: one produced with imaginary scator algebra and the other generated with real scator algebra.

English
  • quadratic mapping
  • visualization
  • puerta de entrada
  • hun
  • ix

Book traversal links for fractales

  • scators
  • Up
  • quadratic mapping

Book navigation

  • fractals
    • quadratic mapping
    • visualization
    • puerta de entrada
    • hun
    • ix
  • real scator algebra
  • imaginary scator algebra
Canal RSS

Language switcher

  • Spanish
  • English

User account menu

  • Log in
Powered by Drupal