Items tagged with mandelbrot

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I am currently working in Maple, following an example on the Maplesoft site very closely. I am trying to make use of the 'Colorize' function in the Escape-Time Fractals package.

I have a Newton's basin with the standard colouring but am trying to make my image more sophisticated. I have tried following the example given for the Mandelbrot set (At the bottom of the page - http://www.maplesoft.com/support/help/Maple/view.aspx?path=Fractals/EscapeTime/Mandelbrot) as there isn't one on the Newton Fracal page but keep receiving the Kernel lost message. I do not think the issue is my firewall.

My code is as follows,

with(Fractals:-EscapeTime);


with(ImageTools);

 

Everything works up until I go to evaluate P. I have tried giving both Arrays datatype=float[8] and have tried getting rid of the datatype section completely as to use the default. Neither of these have helped.

Any insight as to why this may be happening would be appreciated.

Using techniques previously used for generating color images of logistic maps and complex argument, attached is a first draft of a new Mandelbrot set fractal image applet.

A key motive behind this is the need for a faster fractal generator than is currently available on the Application Center as the older Fractal Fun! and Mandelbrot Mania with Maple entries. Those older apps warn against being run with too high a resolution for the final image, as it would take too long. In fact, even at a modest size such as 800x800 the plain black and white images can take up to 40 seconds to generate on a fast Intel i7 machine when running those older applications.

The attached worksheet can produce the basic 800x800 black and white image in approximately 0.5 seconds on the same machine. I used 64bit Maple 15.01 on Windows 7 for the timings. The attached implementration uses the Maple Compiler to attain that speed, but should fall back to Maple's quick evalhf mode in the case that the Compiler is not properly configured or enabled.

The other main difference is that this new version is more interactive: using sliders and other Components. It also inlines the image directly (using a Label), instead of as a (slow and resource intensive) density plot.

Run the Code Edit region, to begin. Make sure your GUI window is shown large enough for you to see the sides of the GUI Table conveniently.

The update image appearing in the worksheet is stored in a file, the name of which is currently set to whatever the following evaluates to in your Maple,

cat(kernelopts('homedir'),"/mandelbrot.jpg"):

You can copy the current image file aside in your OS while experimenting with the applet, if you want to save it at any step. See the start of the Code Edit region, to change this filename setting.

Here's the attachment. Comments are welcome, as I'd like to make corrections before submitting to the Application Center. Some examples of images (reduced in size for inclusion here) created with the applet are below.

When Benoit Mandelbrot was still alive I sent him an email:

Hi,
I am writing to you because I have trouble understanding why
the covariance function in the Fractional Brownian Motion (FBM) is given by:

(t[i]^(2*H)+t[j]^(2*H)-abs(t[i]-t[j])^(2*H))/2)

I would be very grateful if you could please explain this to me in simple and step by step terms.
I understand simple ARIMA models (P(t)=P(t-1)+E(t) where E(t)=p*E(t-1)+r(t)) which have the
same...

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