Funny fleas
There is a notion of infinite regression in logic that describes a process of change that goes on and on and never stops. A graphic example for this phenomenon gives a funny verse about fleas ascribed to Scottish mathematician August de Morgan (19 century):
|   | Great fleas have little fleas upon their backs to bite ‘em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on.
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This story tells us about an infinite increase (reduction) of the size of fleas living on each other. We will illustrate some of the stages of this process using AKVIS Magnifier, a program for image resizing.
- Step 1. Launch the program AKVIS Magnifier.
- Step 2. Open the original image with a double click of the left mouse button on the Image Window. The image is small and fits into the Image Window (the current scale is 100%).
Original image
- Step 3. Activate the Autorun mode
for the program to process the image automatically, every time you change the settings.
- Step 4. Reduce the image twice. For this purpose set the new size into the New Size field: select percent in the drop-down menu and enter 50 into the Width or into the Height field and press the Enter-key.
The program will scale the image to the original image size (the current scale is 200%), so you can compare the images by switching between the Before and After tabs with Tab-key or with the left mouse button.
Reduce the image twice
- Step 5. Save the image as little-flea.jpg by clicking on
and entering a name for the file into the Save as field. Before the image is saved, the whole image will be processed (like with a click on ).
- Step 6. Reduce the image by 4 times. Enter 25 into the Width or into the Height field and press the Enter-key (as the image is already in the workspace, we do not need to load it again). The current scale is about 400 percent.
Reduce the image by 4 times
When switching between the tabs, you will notice that the reduced copy is a bit faded. To improve the image quality on the scales lower than 100% use the Unsharp Mask parameter. The parameter settings can be applied with a click on the corresponding check-box. In this case the original color range is restored with the default settings of Amount = 30 and Radius = 1,5.
Before and After application of Unsharp Mask
- Step 7. Save the result as little-little-flea.jpg (see Step 5).
- Step 8. Increase the original image twice: enter 200 into the Width or into the Height field and press the Enter-key. The image will be processed with default settings (AKVIS Default preset) and will be scaled to 100%. You can increase the value of the Sharpen Edges parameter to 20 to improve the sharpness of the image.
Increase the original image twice
- Step 9. Save the result as big-flea.jpg (see Step 5).
- Step 10. Restore the default values. For this purpose select AKVIS Default in the Presets list.
- Step 11. Increase the original image by 4 times: enter 400 into the Width or into the Height field and press the Enter-key. The image will be processed with the current settings and scaled to 100%.
Increase the image by 4 times
- Step 12. Use the advanced parameters on the Settings Panel to fine tune the result. Compare the result and the original image to find the optimum settings.
«Weak» settings:
Adjust the Microline parameter. As the image contains many thin strokes, you can use a high value of the parameter (370).
Smoothen the edges (Edge Smoothness = 5).
«Strong» settings:
Increase the value of Sharpen Edges to 40-50 to keep more details. The thin lines will become a bit sharper, too.
Reduce the value of Simplicity to 100, so that the result remains close to the original image.
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| Scaled fragment |
Influence of «weak» settings |
Influence of «strong» settings |
- Step 13. Save the result as big-big-flea.jpg (see Step 5).
- Step 14. Close the program AKVIS Magnifier with a click on
.
Fleas biting each other.
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