Manual Fractal Settings of Fracthunder 2.1

fractal algoritms, formulas and parameters

You can choose the formula in the dialogbox of fractals settings:


The scanning of fractals

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:

  1. Inside: the count of step (or iterations) needed to go "nearby" a finite attractor.
  2. Outside: the count of step (or iterations) needed to go "nearby" a infinite attractor.
  3. Max Depth: No (in)finite attractor is reached "nearby" in a defined Maximal count of interations.
When the outcome in Inside or Outside, a factor is defined by the count of steps divide by the specified maximal count of iteratortion. For example, when the Maximal count of iterations is 300, and 75 steps is needed to go to "nearby" an attractor the "factor" is 25%. This "factor" is used to specify a color for that internal pixel.


In de fractal above, the orange pixels are "Inside", the black pixels are "Max Depth", and the blue pixels are "Outside".

Maximal count of iterations per pixel

To maximize the time to take generating the fractal, you must specify the maximal count of iterations per pixel:





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"



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"

the infinite attractor
The Outside Circle; distance from (0,0)

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".


trimming the outside factor: powering and multiplying

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.


trimming the outside factor: in between steps

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


translate value to color

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).


specify settings for the infinite attractor

  • Press or choose in the menu:Fractal | Fractal Properties....
  • In the new dialogbox select tab Outside.
  • Specify in field Outer Circle the radius of the circle.
  • Choose under Sensitivity how the factor is powered:
  • The result is multiplied by value in field Strength.
  • Choose option Continue to calculate the in between steps, or Discontinue to stay with whole number of steps. The whole number of steps is always used for formulas other than the form "z^(2,3,4 or n) + c"
  • In group Depth Color you can specify how the color for the internal pixel is searched.
  • Press button [OK].

  • The difference between Continue and Discontinue Colors:


    Discontinue Colors
    (Outer Circle: 1000)

    Continue Colors
    (Outer Circle adapted to: 100000000) to undo moving colors.


    Continue Colors
    (Outer Circle still: 1000)
    Colors are moved.

    There are many possebilities using the Strenth and Sensitivity. The best is to give examples, so you can see the effect of these setting. Others settings are used in the following dialogbox:



    The following colorpalette is used for "outside" pixels:


    By changing only the Sensitivity and Strength, you get the following pictures:


    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.



    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.




    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




    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.

    A Color palette has a incredible effect how the fractal looks like. The same fractal as above, but using another color palette:



    the finite attractors
    The delta step

    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.


    trimming the inside factor: powering and multiplying

    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.


    Cycling between two or more finite attractors

    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.


    translate value to color

    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).


    specify settings for the finite attractors

  • Press or choose in the menu:Fractal | Fractal Properties....
  • In the new dialogbox select tab Inside.
  • Specify in field Delta Distance the distance between the current points and one of the previous points to detect as "nearby".
  • Specify in field Max Cycle to Detect the maximal cycle value, the count of prevous points which are looked for the delta distance. You can disable detecting for inside pixels, by specify value "0".
  • Choose under Sensitivity how the factor is powered:
  • The result is multiplied by value in field Strength.
  • In group Depth Color you can specify how the color for the internal pixel is searched.
  • Press button [OK].

  • 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.





    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.

    Because for many "inside" pixels, there are more combinations cycle count and iteration count possible, there a more possible colors for one pixel. For almost all pixels in one circle, the same story is valid. So changing the inside settings can affect whole cirles .
    If you increase the Maximal count of cycles, or Maximal (count of) Depth (iterations) and select Priority for highest Cycle it is possible that the color of a circle kan switch to a very different other value