Julia set

Figure D.l A 2-D slice of a 4-D quaternion Julia set. (Computer rendering by the authot.)...

This is an inner loop used in the same spirit as in traditional Julia set computations. No complex numbers are required for the computation. Hold three of the coefficients constant and examine the plane detemined by the remaining two. This code runs in a manner similar to other fractal-generating codes in which color indicates divergence rate. rmu is a quaternion constant. 

Given different values of c one can obtain different Julia sets (Fig. 11). 

Some of the most artistic examples of escape-time fractals explored in the past have been Julia sets, fractal representations describing the behavior of the map mew = -I- c, where z and c are complex numbers." In terms of x and y this map is... 

Gaston Maurice Julia masterpiece entitled Memoire sur F iteration des fonctions dealt with the iteration of a rational function. The following fractals belong to the Julia set (Figure 13.17). 

FIGURE 13.17 Visual presentations of the Julia sets. (Generated by the ManpWin v2.8. http // www.deleeuv.com.au. With pemtission.)... 

Julia Set Boundary of the set of points of a function z that escape into infinity under repeated iteration by f(z). 

Benoit Mandelbrot, French mathematician, pioneer of fractal geometry, and author of the book The Fractal Geometry of Nature (1982). Mandelbrot, who worked at IBM for over thirty years, used a computer to plot images of fractals called Julia sets in 1979. (Hank Morgan / Photo Researchers, Inc.)... 

It is extremely challenging to identify the underlying formation mechanism of the basic seahorse-like pattern. The pattern resembles some local areas within a seahorse valley defined by the Julia set from a pure mathematical mapping of the function in a complex space ... 

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