that is a rather useful feature of fractint. A few notes on the Euler Heun method , the values p and h are limited to the range 0 < h Here's the image you requested in your post (forwarded

below). The bailout value is 64, which was taken from the original parameter file on the FreeBasic site: |z|http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq5.gif (Click image to defeat browser resampling.)

and here it is anti-aliased:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq6.jpg [1]

I

also zoomed in 4X on the lower left corner of your

specified area: The color map is included in this version.

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq7.jpg [2]

The

above 4X zoom, anti-aliased:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq8.jpg [3]

I

don't know whether this is useful to your investigation

of the Volterra-Lotka (V-L) fractal or not, but Fractint's Color Editor has the ability to show only those areas of a fractal that have a specified iteration count / color.

I screen captured a few examples of specific iteration counts using the 4X zoomed version of the V-L fractal you specified.

Note: The white dots in the fractal are a result of the Color Editor's temporarily grabbing two colors (color table entries 254 and 255) to draw its window and

text with, and can be ignored.

Here's the V-L fractal with only the

pixels of value 0 (iteration

count=0) in lailac:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex00.jpg [4]

Pixels of value 1 in green: (I don't see any.)

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex01.jpg [5]

Pixels of value 2 in red: (I don't see any.)

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex02.jpg [6]

Pixels of value 3 in brown: (Finally the fractal shows some pixels

of three iterations...)

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex03.jpg [7]

Pixels of value 4 in orange:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex04.jpg [8]

Note: the digit just to the right of the upper colored tile is the

number of iterations of the pixels in the image colored this color.

I "hand colored" the color table's tile to a contrasting color.

Pixels of value 5 in red in the zoomed 4X image:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex05.jpg [9]

Pixels of value 5 in red in the *original size* image:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex05a.jpg [10]

Pixels of value 6 in green in the zoomed 4X image:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex06.jpg [11]

Pixels of value 6 in green in the *original size* image:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex06a.jpg [12]

Pixels of value 7 in yellow in the zoomed 4X image:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex07.jpg [13]

Pixels of value 8 in hot pink in the zoomed 4X image:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex08.jpg [14]

Pixels of value 9 in cyan in the zoomed 4X image:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex09.jpg [15]

Pixels of value 10 in the original blues.map blue in the zoomed 4X image: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex10.jpg [16]

Pixels of value 20 in in the zoomed 4X image: I see some pixels of value 20 starting to appear in the "sloping line"...

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex20.jpg [17]

Pixels of value 30 in in the zoomed 4X image:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex30.jpg [18]

Pixels of value 40 in in the zoomed 4X image:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex40.jpg [19]

A trick I discovered that's handy to very quickly switch between

several images you're viewing, is to put the images in adjacent

tabs in the leftmost tabs of your browser. (You can drag the tabs to the left if they're not there already.) This trick works in several Windows-compatible browsers.

The key combination , where n is the number of the tab, switches to displaying that tab's contents.

I put these three images in my browser's first three tabs:

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex07.jpg [20]

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex08.jpg [21]

http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex09.jpg [22]

(Don't forget to click each image...)

then held the key down and

quickly typed: 1, 2, 3, 1, 2, 3,...

to see the relationship between areas of the fractal with 7, 8, and 9 iterations.

Sciwise, is this info useful for your investigation? hallane@earthlink.net

########################

-----Original Message----- From:

Fractint

[mailto:fractint-bounces+hallane=earthlink.net@mailman.xmission.com [23]] On

Behalf Of sciwise@ihug.co.nz [24] Sent: Monday, November 23, 2015 2:39 AM To: Fractint and General Fractals Discussion

Subject: [Fractint] Volterra Lotka ph ex

Using Hal Lane's formula ,

where p and h are settable

parameters try :

p 1.768736 h 0.5013054

use the default values for corners.

Top Left X 0 y 4.5 Bot-r X 6 y 0

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Fractint mailing list Fractint@mailman.xmission.com [26]

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Links: ------ [1] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq6.jpg [2] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq7.jpg [3] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtRq8.jpg [4] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex00.jpg [5] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex01.jpg [6] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex02.jpg [7] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex03.jpg [8] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex04.jpg [9] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex05.jpg [10] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex05a.jpg [11] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex06.jpg [12] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex06a.jpg [13] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex07.jpg [14] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex08.jpg [15] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex09.jpg [16] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex10.jpg [17] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex20.jpg [18] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex30.jpg [19] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex40.jpg [20] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex07.jpg [21] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex08.jpg [22] http://www.emarketingiseasy.com/TESTS/Fractals/VltLtIndex09.jpg [23] mailto:fractint-bounces+hallane=earthlink.net@mailman.xmission.com [24] mailto:sciwise@ihug.co.nz [25] mailto:fractint@mailman.xmission.com [26] mailto:Fractint@mailman.xmission.com [27] https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint [28] https://www.avast.com/antivirus