Pair impair


This HTML page describes the different parameters you can find in the mde - Pair impair formula. For further explanations or just suggestions, you may contact me at mdessur@hotmail.com.

I would also mention that English is not my first language. So, I would appreciate comments on how to better this text from that point of view. Thanks.


The formula

The principle behind the Barnsley formula in Fractint is the following: I made the Pair impair formula to see this instead: The calculation is also different in each Barnsley formula and this is what causes their differences. In Pair impair, I have tried to keep this difference. I have also kept both a Mandelbrot & Julia version, so the UF switch option can still be used.

Here are the specific parameters of the formula:
 
Odd-even Type This is the choice between the three corresponding original Barnsley formulas.
Choices First (default), Second, Third, Fourth, Fifth, Sixth, Real, Imag, Real*imag, Real+imag, Diff, Angle, Magnitude, Path, Iteration
Comments The First option corresponds to the Barnsley 1, the Second to the Barnsley 2 and the Third to the Barnsley 3.

The Fourth, Fifth and Sixth options corresponds on fantasies on the first three ones.

The other options are like following:

  • Real - the real part of Z will be used.
  • Imag - the imaginary part of Z will be used.
  • Real*imag - the real part of Z times the imaginary part will be used.
  • Real+imag - the real part of Z plus the imaginary part will be used.
  • Diff - the distance between Z and the previous Z
  • Angle - the angle of Z to the origin
  • Magnitude - the magnitude of Z
  • Path - the approximate length of the orbit at Z
  • Iteration - the number of iterations at Z

  •  
    Odd-even Factor This is a factor that must be applied to determine if we have an odd or even number.
    Choices Ceil (default), Floor, Trunc, Round
    Comments Only integer numbers may be odd or even and with fractals, numbers have always a decimal part. So, we must remove this one and there are four ways to do it: ceiling, flooring, truncating and rounding. 
    • By ceiling, you take the higher next integer (ex: 3.1416 will give 4, -3.1416 will give -2);
    • by flooring, you take the smaller next integer (ex: 3.1416 will give 3, -3.1416 will give -4);
    • by truncating, you just truncate the decimal part (ex: 3.1416 will give 3, -3.1416 will give -3);
    • by rounding, you just round up (ex: 3.1416 will give 3, 3.5416 will give 4, -3.1416 gives -3, -3.5416 gives -2).

     
    Apply Odd-even Sign? By this option, we may ask to consider or not the sign of the number to be turned as an integer
    Choices Enabled, Not enabled (default)
    Comments Results of removing the decimal part are different if we take care of the sign or not. See above the examples for the four different ways to get an integer number.

     
    Seed This is just a set of two numbers you may use to modify the formula in the Julia version. The meaning is purely mathematical.
    Choices You may use any number.
    Comments This number can be determined by using instead the Mandelbrot version and the switch mode.

     
    Starting Point This is just a set of two numbers you may use to start the calculation in the Mandelbrot version. The meaning is purely mathematical.
    Choices You may use any number.

     
    Odd-even Function This is the function that can be applied.
    Choices All the standard functions you may use in UF parameters. Default is ident, which means no function applied.

    The other parameters are part of the Epsilon Range Parameter Toolbox and the Bailout Parameters Toolbox.