Home modified by Ronald Naber

Ronald Naber — Mon, 08 Aug 2016 09:00:37 -0000
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-Welcome to your wiki!
+#Hénon map browser
+### Contents
+* Introduction
+* Quick-start
+* Settings dialog
+* Animations
+* Orbit map mode

-This is the default page, edit it as you see fit. To add a new page simply reference it within brackets, e.g.: [SamplePage].
+### Introduction
+This program is for exploring the Hénon map, which is defined by:

-The wiki uses [Markdown](/p/henon-browser/wiki/markdown_syntax/) syntax.
+x[n+1] = 1 + y[n] - a * x[n]²
+y[n+1] = b * x[n]

-[[members limit=20]]
-[[download_button]]
+A map definition such as this one is used in the field of discontinuous time-dynamics. Starting from initial conditions (x0, y0) and parameters (a, b) the map tells you what the system (x, y) will look like for n = 1, 2... (n to n+1 stands for an increase of time, such as a second or an hour).
+
+After start-up the program calculates one or more orbits in the basin of the Hénon attractor and you get to see the resulting strange attractor of the Hénon map (with parameters a = 1.4, b = 0.3). The calculation stops automatically when the maximum iteration limit has been reached, which depends on window size, area size and the number of CPU's available. 
+
+### Quick-start
+A quick overview of the program features:
+*Zoom in* Look at a portion of the screen by selecting an area. The selection will trigger a new calculation and points that end up in the selected area are shown. You can zoom in on the Hénon attractor indefinitely and all the while the image remains similar, but unlike Mandelbrot fractals, the calculation time increases sharply with zoom-factor. Press F5 or use right mouse click to zoom out again.
+*Show full-screen* Press 'F' to toggle the full-screen mode. 
+*Change Hénon map parameters* Press 'S' to open a settings dialog. 
+*Run animations of the attractor* You can view the Hénon map as its parameters are changing. See the Animation section for details. 
+*Generic actions*
+- Stop current calculation with 'X'
+- Re-draw the current screen with 'R' 
+
+### Settings dialog
+The settings dialog can be opened by pressing 'S'. In it you can define the Hénon parameter values that you would like to try, define animations (in which the Hénon parameter values are varied) and set some calculation parameters. Please see the next section about animations. 
+
+**General settings**
+The definition of a and b is straightforward, but keep in mind that some settings may not yield a stable attractor or not even any periodic behaviour, so the screen may remain empty. 
+
+For control over the calculations it is possible to define the maximum number of iterations for each thread and define the iteration interval after which the result is plotted to screen. By default these settings are determined automatically by the program, which calculates optimized settings based on the window size, zoom-level and the number of availabe threads. The user can disable the auto-mode and set their own values. Please keep in mind that some sanity checks are done before the calculation is started, so the program may change the entered settings. 
+
+**Animation settings**
+In the animation tab one can set the mid-point, range and increment for Hénon parameters a and b in order to define the animation settings. You can also select whether you want to animate either a or b or both at the same time. The animation will start at (midpoint - 0.5 * range) and end when the range limit has been reached. 
+For animations it is necessary to lower the maximum number of iterations compared to those used for viewing still images, so these values can be defined separately and have lower default values. The minimum time delay between each animation frame can be set. The actual delay may be longer depending on how long it takes to calculate each frame.
+
+For certain a,b values there will be periodic behaviour, which means that only a few pixels will show up on the screen. Single pixels can be hard to see so this is why there is an option to enlarge such rare pixels. If there are between 1 and 16 pixels in total during any screen update then each one will be enlarged to 5 pixels for better visibility. 
+
+**Orbit map settings**
+In orbit map mode the horizonal axis represents a parameter (a or b) and the vertical axis a coordinate (x or y). In this screen one can choose the parameter and coordinate to use and one can set some calculation settings. It is possible to change the plot interval and the max iterations that will be used for each pixel/parameter value along the screen width. The plot interval value only does something when OpenCL is enabled. 
+
+**Calculation settings **
+*Drop iterations* The number of dropped iterations that are performed for each thread can be set here. Each calculation thread starts from x,y values that are chosen randomly in the range of (-0.1,0.1), so that each thread can follow an independent path along the attractor, but the first few hundred iterations may not have reached the attractor yet, so this is why the program performs a few hundred iterations before it starts passing the information to the screen. 
+
+*Thread count *The program runs several threads at the same time by default in order to speed up the calculations. By default the thread count is equal to the number of CPU's detected, but it can be set to a lower value. 
+
+*Enable OpenCL* There is support for OpenCL for CPU/GPU multithreading. The OpenCL functionality can be enabled if the PyOpenCL Python module can be loaded successfully, which may require appropriate drivers for each OpenCL platform (Intel/AMD/NVIDIA). One or more devices need to be selected to run the calculations on. Not all devices or device combinations may work well, but the program will give a message if this occurs. 
+
+### Animations 
+The program has default animation settings that can be activated in the settings dialog by clicking on the 'Animate' checkboxes for parameter a or b. The animation can then be started in the main screen by pressing 'A'. These default animations demonstrate some general aspects of the Hénon map. For parameter 'B' the animation starts with a stable point that doubles its period a few times before it grows into the Hénon attractor. For parameter 'A' the animation features look similar but it also shows a crisis, i.e. the sudden disappearance of the attractor near a = 1.2. When the attractor has formed almost fully you may notice that the attractor disappears again a few times. These must be periodic windows where there is a brief reappearance of periodic behaviour 
+
+### Orbit map mode 
+In orbit map mode the horizontal axis represents a parameter (a or b) and the vertical axis a coordinate (x or y). It is another way of visualizing the Hénon attractor and is especially suited for showing the bifurcations and appearance and disappearance of chaotic behaviour. By default, the selected parameter is 'a' and the vertical coordinate is 'y'. It is possible to zoom-in on the image by selecting an area with the mouse. Right-click or 'F5' resets the view to the default setting.
Discussion for Home page

Ronald Naber — Mon, 08 Aug 2016 08:47:43 -0000
test
Home modified by Ronald Naber

Ronald Naber — Sun, 07 Aug 2016 15:59:18 -0000
Welcome to your wiki!
This is the default page, edit it as you see fit. To add a new page simply reference it within brackets, e.g.: [SamplePage].
The wiki uses Markdown syntax.
Project Members:

Ronald Naber (admin)
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Home modified by Ronald Naber

Discussion for Home page

Home modified by Ronald Naber

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