Fractaldraw 2.2
Free Version
Publisher Description
This app allows you to draw the Julia set of any rational function by simply fixing the number, position and character (attractive or repulsive) of fixed points in the complex plane. You don’t have to put in any formula! If you put a new fixed point the corresponding Mandelbrot set is shown which tells you in which regions the fixed point is attractive or repulsive.
(For experts: The character of the fixed points is structured by Newton’s method to find the zero of a factor (z-z_f)^p.
In this way the ordinary Julia sets of the quadratic iteration are obtained by putting one fixed point with p=-0.5 and varying a second around p=0.5.)
But you don`t have to know any mathematical details. Just play around with position number and character of fixed points and try to understand intuitively their impact on the obtained picture.
In this way you can draw really beautiful self similar structures and discover intuitively results which are partially not understood and may be not even known by actual mathematical research.
To get an idea how this works just press the "+" button at the beginning (you know have 3 fixed points). Then choose "make figure symmetric" in the menu (In this way you obtain the famous fractal for finding the zeros of z^3-1 with Newton’s method). By varying the position of the cross in the lower window you change the character of one of the fixed points and you can find an astonishing variety of fractal figures. Especially the black cusps at the border of the Mandelbrot set are leading to interesting structures.
The colorgradient is changed with the volume up/down buttons of your phone.
In addition you can explore the Mandelbrot and Julia sets of the quadratic, cubic and sine fractal.
Very remarkable is the possibility of exploring the Collatz fractal which is connected to the famous Collatz conjecture.
Search for small parts in the Mandelbrot set of the Collatz fractal where you can find copies of the well known Mandelbrot set of the quadratic iteration. Then search for a small region of the Julia set which is connected to the copy of the Mandelbrot set.
You will find that the small Mandelbrot sets are embedded in an astonishing variety.
All of this is produced by the iteration of f(z)=c*z+1/4-((c-1/2)*z+1/4)*cos(pi*z) !!
About Fractaldraw
Fractaldraw is a free app for Android published in the Teaching & Training Tools list of apps, part of Education.
The company that develops Fractaldraw is Florian Jasch. The latest version released by its developer is 2.2.
To install Fractaldraw on your Android device, just click the green Continue To App button above to start the installation process. The app is listed on our website since 2016-12-06 and was downloaded 2 times. We have already checked if the download link is safe, however for your own protection we recommend that you scan the downloaded app with your antivirus. Your antivirus may detect the Fractaldraw as malware as malware if the download link to flo.newton is broken.
How to install Fractaldraw on your Android device:
- Click on the Continue To App button on our website. This will redirect you to Google Play.
- Once the Fractaldraw is shown in the Google Play listing of your Android device, you can start its download and installation. Tap on the Install button located below the search bar and to the right of the app icon.
- A pop-up window with the permissions required by Fractaldraw will be shown. Click on Accept to continue the process.
- Fractaldraw will be downloaded onto your device, displaying a progress. Once the download completes, the installation will start and you'll get a notification after the installation is finished.
