2011/02/11: Fixed a bug with the rendering of
rectangles vs ovals and added stacks that
show the growth at various stages for comparison.
2012/04/18: Fixed problem with no image
appearing on screen; responded to user request to retain
arrays while working on a model; added “About” message
2015/01/18: Fixed bugs reported with spiral model and GUI.
Buttons now show the selected model. Added requested feature to
render a model without always having to configure it.
Added requested feature to specify the image size.
2015/01/20b1239: Fixed bug requests so that coefficient
files now load properly and on screen progress display runs
This plugin draws iterated growth models for multifractal
analysis in ImageJ (e.g., using FracLac for ImageJ).
These are saveable screen drawings made of points calculated using the basic expressions:
xn+1 = mxnXxpow
+ nynXypow + o and yn+1 = fxnYxpow +
gynYypow + h.
For each model,
each equation’s coefficients (m,n,o;f,g,h; Xxpow, Xypow, Yxpow, Yypow) are
specified in sets that the user can modify.
Each of these sets also contains a probability of using the
set. This is for cases when more than one set of coefficients
is used to calculate each point, chosen according to a likelihood
that the user sets.
Each particle calculated and drawn is coloured on a
background, and all
are the same size. The user can specify to use
a single colour or gradient, and can set the gradient, foreground,
The user can change the size of the particles
in the models using an option in the first popup.
There are five default models. The user
can change the coefficients to vary
the basic pattern, or
change the number of sets to create a new model.
“Henon” model is specified by one set of coefficients (i.e.,
the likelihood of using that set is 1).
The Henon Map model is a multifractal benchmark model;
it is also specified by one set of
coefficients. It has a (capacity) fractal dimension that is
assumed to be around 1.261
(correlation dimension around 1.25).
The “Random” model is similar to the Henon models, but uses
two sets of coefficients and probabilities.
The “D. Greene Fern” model uses four sets
of coefficients. It is from an algorithm by
David Greene (Charles Sturt University),
The custom model is
essentially the same as the fern, with a few changes
in coefficients and probabilities.
Using the plugin
To generate a default model, the user selects a model from
the menu on the GUI (see the screenshot),
then clicks a button at the bottom to render the model
or reconfigure prior to rendering. In the second case,
various dialogs will appear asking the user to specify some settings.
The user can also save or load files of coefficients using the
checkboxes and buttons on the interface.
When configuring, popups appear displaying
the coefficients for each set, which the user can
modify as desired.
At the bottom of each set, there is a space for
the probability that the coefficients above it
will be used in generating each next point. The total of
all probabilities should not be greater than 1;
all sets for values
that make the cumulative total greater than 1 are ignored.
Animations There is a setting to generate
stacks showing the progression.
The stacks can be saved as avis or analyzed individually
to quantitate multifractal scaling at different stages.
Author: Wayne Rasband (wsr at nih.gov) Date: 2003/09/12 Requirements: ImageJ 1.31h or later Source: Animated_Sine_Wave.java Installation: Download Animated_Sine_Wave.java to the plugins folder, run it using
Authors: Edwin Donnelly (edwin.donnelly at vanderbilt.edu) Frederic Mothe (mothe at nancy.inra.fr) History: 2007/10/30: First version 2008/03/10: Improvements by Frederic Mothe: The default center for the