4.2 / April 18, 2017
(3.6/5) (49)
Loading...

Description

This app allows you to draw the Julia set of any rational functionby simply fixing the number, position and character (attractive orrepulsive) of fixed points in the complex plane. You don’t have toput in any formula! If you put a new fixed point, the correspondingMandelbrot set is shown which tells you in which regions the fixedpoint is attractive or repulsive. For experts: The character of thefixed points is structured by Newton’s method to find the zero of afactor (z-z_f)^p.But you don`t have to know any mathematicaldetails. Just play around with position number and character offixed points and try to understand intuitively their impact on theobtained picture.In this way you can draw really beautiful selfsimilar structures and discover intuitively results which arepartially not understood and may be not even known by actualmathematical research.To get an idea how it works choose the firstexample in the example gallery or press reset. You are now startingwith two attractive fixed points. Press the brush button to see theactual positions of the fixed points.The button with the Mandelbroticon shows you the Mandelbrot set corresponding to the actual fixedpoint indicated by a cross.Changing the position of the cross inthe Mandelbrot window below you can change the textures in thefixed point environments of the Julia set. Choose "fixedpointproperties" to see the power p which characterizes the fixed point(attractive if the real part is smaller than 0.5 or repulsive ifthe real part is larger than 0.5).For example a nice texture isobtained for p=0.8.Note that the Mandelbrot set is a map oftextures of the Julia set!Tip the second fixed point indicated by acircle (which then switches to a cross) to see its correspondingMandelbrot set and to change its properties by varying the positionof the cross in the lower window.In this way you can obtain thethird example if you choose p=0.8 for the first fixed point andp=-0.219+i*0.611 for the second (zoom in the upper window to seethe full structure).Press the brush to disable the change of fixedpoint positions before you zoom. By varying the position of thecross in the lower window you change the character of the actualfixed point and you can find an astonishing variety of fractalfigures. Especially the black cusps at the border of the Mandelbrotset are leading to interesting structures.With the "+/-" button youcan increase/decrease the number of fixed points in thenewtonfractal mode . If you Choose "make figure symmetric" in themenu you obtain the famous fractal for finding the zeros of z^n-1with Newton’s method if you putted n fixed points before.Varyingnumber position and character (textures) of the fixed points youcan use the app to draw a very large variety of self similarfractal structures. The texture of a fixed point is changed if youswitch on its corresponding Mandelbrot set. Note that it is anintrinsically mathematical problem that the Mandelbrot setsometimes switches strangely!This happens when the algorithm findsa different critical point (point with zero derivative of theiteration function). The example gallery serves as an inspirationof what can be done. But with some experience you can create muchmore interesting artwork. With the "save project" option it ispossible to save editable and zoomable projects to work onfurther.Tip long on a project to delete it. You can also explorethe Mandelbrot and Julia sets of the fractals corresponding to theiteration functions z^n+c for any power n.Just choose the famousquadratic mandelbrot set (last example) in the example gallery andpress the "+" or "-" Buttons to increase or decrease the power n.

App Information Fractaldraw

  • App Name
    Fractaldraw
  • Package Name
    flo.newton
  • Updated
    April 18, 2017
  • File Size
    2.0M
  • Requires Android
    Android 3.0 and up
  • Version
    4.2
  • Developer
    Florian Jasch
  • Installs
    10,000+
  • Price
    Free
  • Category
    Education
  • Developer
  • Google Play Link

Florian Jasch Show More...

Fractaldraw 4.2 APK
Florian Jasch
This app allows you to draw the Julia set of any rational functionby simply fixing the number, position and character (attractive orrepulsive) of fixed points in the complex plane. You don’t have toput in any formula! If you put a new fixed point, the correspondingMandelbrot set is shown which tells you in which regions the fixedpoint is attractive or repulsive. For experts: The character of thefixed points is structured by Newton’s method to find the zero of afactor (z-z_f)^p.But you don`t have to know any mathematicaldetails. Just play around with position number and character offixed points and try to understand intuitively their impact on theobtained picture.In this way you can draw really beautiful selfsimilar structures and discover intuitively results which arepartially not understood and may be not even known by actualmathematical research.To get an idea how it works choose the firstexample in the example gallery or press reset. You are now startingwith two attractive fixed points. Press the brush button to see theactual positions of the fixed points.The button with the Mandelbroticon shows you the Mandelbrot set corresponding to the actual fixedpoint indicated by a cross.Changing the position of the cross inthe Mandelbrot window below you can change the textures in thefixed point environments of the Julia set. Choose "fixedpointproperties" to see the power p which characterizes the fixed point(attractive if the real part is smaller than 0.5 or repulsive ifthe real part is larger than 0.5).For example a nice texture isobtained for p=0.8.Note that the Mandelbrot set is a map oftextures of the Julia set!Tip the second fixed point indicated by acircle (which then switches to a cross) to see its correspondingMandelbrot set and to change its properties by varying the positionof the cross in the lower window.In this way you can obtain thethird example if you choose p=0.8 for the first fixed point andp=-0.219+i*0.611 for the second (zoom in the upper window to seethe full structure).Press the brush to disable the change of fixedpoint positions before you zoom. By varying the position of thecross in the lower window you change the character of the actualfixed point and you can find an astonishing variety of fractalfigures. Especially the black cusps at the border of the Mandelbrotset are leading to interesting structures.With the "+/-" button youcan increase/decrease the number of fixed points in thenewtonfractal mode . If you Choose "make figure symmetric" in themenu you obtain the famous fractal for finding the zeros of z^n-1with Newton’s method if you putted n fixed points before.Varyingnumber position and character (textures) of the fixed points youcan use the app to draw a very large variety of self similarfractal structures. The texture of a fixed point is changed if youswitch on its corresponding Mandelbrot set. Note that it is anintrinsically mathematical problem that the Mandelbrot setsometimes switches strangely!This happens when the algorithm findsa different critical point (point with zero derivative of theiteration function). The example gallery serves as an inspirationof what can be done. But with some experience you can create muchmore interesting artwork. With the "save project" option it ispossible to save editable and zoomable projects to work onfurther.Tip long on a project to delete it. You can also explorethe Mandelbrot and Julia sets of the fractals corresponding to theiteration functions z^n+c for any power n.Just choose the famousquadratic mandelbrot set (last example) in the example gallery andpress the "+" or "-" Buttons to increase or decrease the power n.
Buddabrot 4.0 APK
Florian Jasch
This is a simple app for drawing the Mandelbrot sets(https://en.wikipedia.org/wiki/Mandelbrot_set) and thecorresponding Julia fractals for the iteration functions z²+c, z³+cand z⁴+c. It uses new algorithms for coloring the escape dynamicwhich leads to extraordinary pictures of the environment of theMandelbrot and Julia fractals. Use the pattern button to change thecoloring algorithm for the escape dynamic.The iteration number isincreased automatically if you zoom to more calculation intensiveparts of the Mandelbrot sets. It can also be changed manually inthe settings.The volume up/down buttons are changing the colorgradient.
Loading...