LHK.ME.UK

Fractal page

Some more recent software that uses modern interactive design and accelerated graphics to allow exploration of the Mandelbrot and Julia sets in real time can be accessed below. To find out more click below to view the instructions. If you have Java installed, you can download and run the software by clicking the button below. The downloaded file will unzip to a folder called JMsoftware, with three sub-folders containing the executable jar file, the Java source code and the license. Part of a Julia set.

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Fractal page | lhk.me.uk Reviews

<META> DESCRIPTION

Some more recent software that uses modern interactive design and accelerated graphics to allow exploration of the Mandelbrot and Julia sets in real time can be accessed below. To find out more click below to view the instructions. If you have Java installed, you can download and run the software by clicking the button below. The downloaded file will unzip to a folder called JMsoftware, with three sub-folders containing the executable jar file, the Java source code and the license. Part of a Julia set.

<META> KEYWORDS

1 new software

2 a barnsley fern

3 a logistic plot

4 a newton basin

5 the mandelbrot set

6 generators

7 koch curve animation

8 quadratic koch animation

9 coupons

10 reviews

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new software,a barnsley fern,a logistic plot,a newton basin,the mandelbrot set,generators,koch curve animation,quadratic koch animation

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Fractal page | lhk.me.uk Reviews

https://lhk.me.uk

Some more recent software that uses modern interactive design and accelerated graphics to allow exploration of the Mandelbrot and Julia sets in real time can be accessed below. To find out more click below to view the instructions. If you have Java installed, you can download and run the software by clicking the button below. The downloaded file will unzip to a folder called JMsoftware, with three sub-folders containing the executable jar file, the Java source code and the license. Part of a Julia set.

INTERNAL PAGES

lhk.me.uk

1

Julia set

http://lhk.me.uk/biglongjulia.htm

The plot on this page is of the Julia set of z. C, with c = -1.76 0.005i. The value of c in this case lies within the miniature version of the Mandelbrot set shown in the plot to the left of this one on the main page. The Mandelbrot set contains many smaller versions of itself, some along its hairs as well as along the needle. The boundary between the coloured area and the black area gives a visual image of where the Julia set lies. Parts of the black (ie non-divergent) area of the Julia plot above a...

2

Mandelbrot

http://lhk.me.uk/bigmandelbrot.htm

The plot on this page is the Mandelbrot set, which is probably becoming one of the most famous images of our times. The Mandelbrot set is defined as the set of parameters c for which the Julia set of z. C is connected. Such values of c are shown in black in the plot above. A well-known theorem states that the Mandelbrot set consists of those values of c for which the iterates of Z n 1. C are bounded when the initial value of z is zero, and this enables plots like the one above to be produced quite easily.

3

mini Mandelbrot

http://lhk.me.uk/bigminimand.htm

This is an enlargement, that is a more detailed plot, of one of the quasi self-similar miniature versions of itself that the Mandelbrot set contains. The Mandelbrot set contains many such smaller versions of itself, including this one which can just be seen on the plot of the whole Mandelbrot set at around -1.76 on the horizontal axis. Some interesting Julia sets of z.

4

fern

http://lhk.me.uk/bigfern.htm

The Barnsley fern is one of the best known images that can be produced by plotting the invariant set of a few transformations of the two dimensional plane. It is the invariant set of the following four contractions:-. X,y) = (0, 0.16y). X,y) = (0.85x 0.04y, -0.04x 0.85y 1.6). X,y) = (0.2x - 0.26y, 0.23x 0.22y 1.6). X,y) = (-0.15x 0.28y, 0.26x 0.24y 0.44).

5

Fractal Scenery

http://lhk.me.uk/bigscene.htm

Most of the images in this drawing were produced by using recursive (ie self-invoking) computer drawing methods. The water's edge is composed of Koch curves, and the lily pads using the curve in figure 9.5. The ferns and their reflections were plotted as invariant sets, the reflections plotted selectively so only the part on the blue water was shown. The tree and grasses and their reflections were drawn using recursive drawing methods.

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Fractal page

Some more recent software that uses modern interactive design and accelerated graphics to allow exploration of the Mandelbrot and Julia sets in real time can be accessed below. To find out more click below to view the instructions. If you have Java installed, you can download and run the software by clicking the button below. The downloaded file will unzip to a folder called JMsoftware, with three sub-folders containing the executable jar file, the Java source code and the license. Part of a Julia set.

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