You can choose the formula in the dialogbox of fractals settings:
To understand some settings, you need to know how the fractal is scanned. The fractal is scanned bij the internal resolution, defined in the dialogbox Properties Fractal in tab Scanning in column Internal. For every internal pixel, there are three kind of outcomes:
To maximize the time to take generating the fractal, you must specify the maximal count of iterations per pixel:
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Color Max Depth: Black
Count Max Depth: 50 For every displayed pixel, one scanned pixel. |
Color Max Depth: Black
Count Max Depth: 80 When change Count Max Depth from 50 to 80, Adapt Outside Strength at Changing Max Depth: "on" |
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Color Max Depth: White
Count Max Depth: 50 |
Color Max Depth: Black
Count Max Depth: 80 When change Count Max Depth from 50 to 80, Adapt Outside Strength at Changing Max Depth: "off" |
When the point is outside that circle with the given radius having its centrum in (0,0), the point is "nearby" the infinite attractor and the iteration for that pixel stops. For most formulas, this circle must be big, for example a radius of 1000, and when it is big the value has no real effect of the displayed fractal. The Outer Circle has other effects for formulas having a divide by a part that contains "z".
When the pixel is indeed categorized als "outside", its value (between 0% and 100%) is first powered using a exponent and the result is multiplied bij Strength.
Normally the count of iterations needed to go "nearby" the infinite attractor, is a whole number,
but When using formulas "z^2 + c", "z^3 + c", "z^4 + c" or "z^n + c",
you can smoothen the colors by interpolating that value by what value it would need to go exactly at the edge on the Outer Circle.
When it would take for example 7 step to go on the edge to that circel,
the value stays 7. But when for example the circle has a radius of 1000 and formula "z^2+c" is used,
and after 7 iterations it the point has a distance of 10000 for (0,0), for formula "z^2+x"
it is expected that after 6 iteration the distance from (0,0) should be 100 (= 10000^(1/2)) (2 comes from the chosen formula),
the interpolated value in this case would be 6.5 because in this very simplified and specific case,
6 + 100_log (10000/1000) = 6 + 100_log 10 = 6 + 0.5 + 6.5
The resulting value is used to give a color to that pixel by pointing in a color palette (0% is most left en 100% is most right),
or interpalating between two specified colors (0% at Background en 100% at Foreground).
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Discontinue Colors
(Outer Circle: 1000) |
Continue Colors
(Outer Circle adapted to: 100000000) to undo moving colors. |
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Continue Colors
(Outer Circle still: 1000) Colors are moved. |
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Sensitivity: Low (exponent = 2)
Strength: 1 Much black and blue (at the beginning of the color palette) because of low value, increasing of Strenth is needed to see more. |
Sensitivity: Low (exponent = 2)
Strength: 6 Much black and blue, but enough lighter colors. High contrast. All colors of the whole color palette. |
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Sensitivity: Normal (exponent = 1)
Strength: 1 Much black and blue, but also much red, increasing of Strenth can create more. |
Sensitivity: Normal (exponent = 1)
Strength: 2.5 Somewhat high contrast. All colors of the whole color palette. |
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Sensitivity: High (exponent = 0.5)
Strength: 1 No more black, because of the high sensitivity (much increasing for low values). Many higher values (yellow and white) |
Sensitivity: High (exponent = 0.5)
Strength: 1.5 Many very high values (light blue and blue in the middle) |
Sensitivity: Normal High (exponent = 0.5)
Strength: 0.7 After decreasing the Strength, there are still details |
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Sensitivity: High (exponent = 0.25)
Strength: 1 Most values are high and very high. less contrast because of the lack of low values. |
Sensitivity: High (exponent = 0.25)
Strength: 1.3 Many highest values (blue). |
Sensitivity: Normal High (exponent = 0.25)
Strength: 0.7 Still no low values, many middle and higher values, but no very high values. Also here is only a part of the color palette used. |
When distance between the current point and the previous point is less than a specified Delta Distance, then the point is "nearby" a finite attractor. For most formulas, this circle must be big, for example a radius of 0.0001, and when it is small the value has no real effect of the displayed fractal.
When the pixel is indeed categorized als "inside", its value (between 0% and 100%) is first powered using a exponent and the result is multiplied bij Strength.
Sometimes, a point is going two more than one attractor, always alternating between these attractors. You cannot detect this by looking at de distance of the current and the previous point. You must look back to more previous points until a specified maximal count of points. When a small enough distance is detected between a point and for example, three points before, so a cycle "3" is detected, and also a count of iterations is found resulting in a Inside Factor. In some cases a point take a combination of cycles, so more combination cycle-count of iterations are found. You can specify which of then should be chosen: the lowest or highest cycle, the cycle with the lowest count of iterations. The first two options costs more time to generate a fractal because you must for each pixel iterate to a maximal count of iterations, because another cycle could be detected until the last iteration.
When a pixel is indeed detected as Inside, you have a combination of the cycle-value (1 or more) and the inside factor
(between 0% and 100% (before trimming))
You can choose to use only the inside factor and point into a color palette (0% is most left en 100% is most right),
or interpolate between the Background Color and Foreground Color (0% at Background en 100% at Foreground).
The Foreground/Background Color (each) can be a fixed color, or a color from the color palette,
in that case the cycle value is point into the color palette: (value 1 at left, and the maximum cycle value at right, when the maximum is 1,
allways the most left color is pointed).
A Mandelbrot fractal has many parts with different count of cycles between finit attractors.
Here the maximal detectable count of cycles is set to 50.
The "Background" Color is set to palette containing rainbow colors.
The "Foreground" color is set to Black.
The great circles has a low count of cycles, so the colors at the beginning of the rainbow palette is used (blue and green-blue),
the small ones are orange and red and have cycle counts between 20 and 40.
The center of the circles has low count of iterations needed to come "nearby" the set of finit attractors, and belongs to the rainbow color palette.
At the edges of the circles towards the maximal count of iterations and belongs to the single color Black.
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Cycle Selection: Priority for lowest Cycle
The yellow bottom circle has a cycle count of 17 and iterations count of 17 in the center. |
Cycle Selection: Priority for highest Cycle
The purple bottom circle has a cycle count of 48 and iterations count of 49 in the center. |
Cycle Selection: Priority for lowest Depth
The yellow bottom circle has a cycle count of 17 and iterations count of 17 in the center. |