Fractal analysis system for Windows

If you are interested, please read NOTE at the bottom of this page.


This software can generate % image of RGB and thinning image, extract red or green area, calculate fractal dimension and coverage, from color image, gray scale, binary, 3D sliced (layer).

Fractal dimension is calculatede by the method of box-counting after preprocessing.

Thinning is used to be 1 pixel thickness when analyzing wave image from image scanner.

Calculated area can be defined.

Relationship between the size of box and the count can be displayed with plot graph. So you can confirm whether the image is fractal or not by linearity. If limited sizes can be used for calculating fractal dimension, any count data can be deleted or edited and recalculate fractal dimension.

Isolated black points can be deleted and median filter can be applied in the case of binary image with much noise.

Fractal dimension of black area in many 3D sliced (layer) images (bmp) can be calculated.

Other image formats (png, pcx, jpg) can be use with Susie plug-in.


Windows with full color display


(1) Open an image file
Open the image file, or make drag-and-drop the file from filer (ex. file explore).

(2) Extract red or green area

According to your object, select "Extract red" or "Extract green" in menu.
Result of green extract
If you can not extract successfully, select "Image processing -> Change threshold".
And change threshold in the panel.

This value is border of chromaticity (%), and default value is 0.

If you want to extract only dark green, this value shoud be big. If you want to extract broad area, this value shoud be minus.

(3) Calculate fractal dimension

Select "Fractal dimension -> Black".
Then the result may be displayed.

Not only fractal dimension, but also size of image, coverage (%), number of data to calculate (n), correlation coefficient (r) are displayed in same window.

These value can be copied to clipboard by the key of CTRL+C.

(4) Area definition

Select menu of "Define area -> Define area" or button of "Define area".
Then track box may be displayed.

You can change the area to be calculated by the movement of mouse cursor on the box line with drag mode.

And you can move the area by the movement of mouse cursor in the box with drag mode.

If you can not success, you may input data directly in the menu of "Define area -> Input value".

Information about size and left top reference of the box is displayed in the upper of the main window.

Fractal dimension of defined area

(5) Fractal dimension of grayscale

Open color image file and select "Image processing -> Gray scale".
Then the image will turn to gray scale.

Select "Fractal dimension -> Gray scale".

Then fractal dimension of grayscale may be displayed.

Note that the item of coverage changes the difference of brightness.

These value can also be copied to clipboard by the key of CTRL+C.

(6) 3D sliced (layer) images

This analysis is to calculate 3D sliced images like the left images.
Select the menu of "Fractal dimension -> 3D sliced",
then the new window will be opened as is shown left.

If there are 9 images sliced, you must rename these images as from 1.BMP to 9.BMP in order. If you can save as PNG format, then rename these images as from 1.PNG to 9.PNG.

Select the file name of the first and last image (here 1.bmp and 9.bmp) , input size per pixel and distance of each image.

Click "perform" button, and the results may be displayed after one moment.

(7) Show the relationship between box size and the count

Select "Fractal dimension -> Display size vs. count".
Then the box size and count data in the left side in the new window, plots and regression line in the right, will be displayed.

Plots graph can become larger or smaller by cliping the border of the window.

This graph is linked with the leftside data. So, if you change, delete or add the data of count, and push "recalc" button, then the graph, correlation coefficient and fractal dimension may be recalculated.


Upper buttons of toolbar are "open bmp", "area definition", "fractal dimension of black area", "fractal dimension except black area", "fractal dimension of grayscale", "Display the box size vs. count" from left to right.

Note that if you can not find rectangle of defined area, twice clicks of "area definition" makes the rectangle appeared in the present window.

"process - reverse"

"process - thinning"
If you want to calculate the fractal dimension of line or curve, you should thin the image before calculating.

"fractal - length of curves in black"
You should thin the image before using this function.


1) SASAKI, H., S. SHIBATA, and T. HATANAKA (1994) : An Evaluation Method of Ecotypes of Japanese Lawn Grass (Zoysia japonica STEUD.) for Three Different Ecological Functions. Bull. Natl. Grassl. Res. Inst. 49: 17-24 (in Japanese with English summary and then version 1.0 was released).

Hiroyuki Sasaki
National Institute of Livestock and Grassland Science


Public researcher or student can use this software for free with filling out two application papers if the purpose is research use. If you are interested, please download the form here (Zipped Rich Text File Format made by MS-Word) and send the Submission and the Agreement by e-mail.
When the submission is accepted, I will send the software attached to e-mail soon.
If you belong to commercial society, utilization of this software will not be permitted.