Genfract 3.1
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    A minor revision mainly issued to correct some small errors, squash some little bugs and make some
 minor improvements. A redrawn Mandelbrot now regains all its capabilities.
   Traditional Inverse Julias have more options and can be coloured by weight. Also, if the random walk is
 drawn by entering sgn(rnd-a1)sqrt(z-c), 0< a1 <1, 'Orbit only' with 180 deg symmetry, it can be coloured
 provided you have checked 'Strange attractor'.

Genfract 3.0
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             The program now contains a parser to enable the user to input their own functions.
 The functions must be explicit and unconditional (no If ... Else ... structures) but they can be complex
 of the form new Z = f ( Z , c ) or real of the form  new x = f ( x , y , c1 ), new y = g ( x , y , c2 )
 and may be indirectly defined by using introduced intermediate variables. The parser is very 'free form'
 and allows the functions to be typed in in the same way as they may ordinarily be written as well as
 accepting a more formal syntax. The range of mathematical functions which can be called on is very
 comprehensive.
    The program allows for the complete Mandelbrot for the user function to be drawn, but this can be a
 very slow business. The problem is finding the critical values. The program can usually manage to do this
 and there is no problem when the critical values are constant, i.e. not dependent on c, meaning that the
 sequence is generated by an equation of the form Z = f ( Z ) + g ( c) or c * f ( Z ) or f ( z ) / c.
 I have not yet dealt with Z = g ( c ) * f ( z ) and I don't promise that I will. But when the critical
 values do depend on c, the equation being genuinely of the form Z = f ( Z , c ), then the critical values
 have to be re-calculated for every new sequence ... and that takes time, a lot of time! There does not
 appear to be any way round this but I believe that these complete figures are so important for the proper
 understanding of what the associated Julias are like that the serious investigator will think the result
 is worth it.
    A 'normal' partial Mandelbrot (calculated from just one critical value, or even worse from some other
 single start point) is just that - partial and obviously an incomplete figure telling just a part of the
 full story and quite misleading in its role as an index to the Julias.
     Sometimes it will not be possible to find critical values - there are never such things for real
 equations. An alternative is to use a fairly large number of test values scattered around a likely looking
 region of the Julias, trying to cover all the possible basins of attraction. This option is incorporated.
 It could be sensible to draw a few Julias first to see where usefully to place the area of test points.
 This is the method which has been used for the Volterra-Lotka map from the earliest days of Genfract.
 Unfortunately this method is also very slow depending on the number of test points.
   I thought it would now possible to draw the convergence fractals for the inverses of Julias, provided
 that you can write the inverse of the function. So for the traditional Julias, Z = Z^2 + c, the inverse is
 Z = sqr ( Z - c ) or alternatively Z = - sqr ( Z - c ). I was a little surprised to find that either choice
 of inverse function gives sequences which converge to one of the fixed points of the transformation
 (or to a periodic cycle if c lies inside the cardioid of the Mandelbrot, in which case one of the two fixed
 points is an interior attractor of the Julia). So in terms of the binary tree formed by the two choices of
 root at each point, keeping left (or right) all the time does not lead to the Julia boundary. To get there,
 you could take the full tree or alternatively take the branches at random. The random walk works O.K. using
 sgn(rand-areal)*sqrt(z-c), 0<areal<1, the development depending on the choice of areal. The attractor is the
 Julia set itself (the boundary) which, being a strange attractor, requires 'Strange attractor' to be set in
 the menu under 'Iteration\Strange attractor'. The result however is no good as a convergence fractal as the
 number of convergence steps is also random. The Julia set is clearly drawn as the attractor, but it appears
 that there is no such thing as a convergence fractal for an inverse Julia! It is more sensible to go
 straight to 'Orbit only'. As Genfract can't deal with a binary tree for a user function yet, I have built
 in the traditional inverse Julias. 

Genfract 2.1
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             This is actually a pretty major revision in spite if its numbering :-

    The problem about failure to refresh has been dealt with.

    The window / frame dialog box has been overhauled.

    When you click on a completed Mandelbrot or Julia you are now given full information about the orbit
 associated with that point such as the fate of the orbit, the number of iterations before convergence or
 divergence, etc.  

    An important technical change concerning the convergence distance has been made.
 This distance is originally set at approximately half a pixel at startup scale using 1024 x 768 resolution.
 On zooming, of course, half a pixel becomes a much smaller distance so it seemed sensible to reduce
 the convergence distance accordingly. Unfortunately, this had the effect of making convergence much
 slower so that the number of iterations had to be increased and also a longer time was taken. So that
 was a bad idea and the convergence distance is no longer changed on zooming - with no detrimental
 effect. Users can change the convergence distance themselves if required.

   The most obvious changes are to the colouring facilities.
      A 'Smooth' option is now available which smooths out the steps into a continuous colour change.
 A 'Waves' option runs through each palette section both forwards and in reverse which removes a
 sudden change of shade when sections are joined and also doubles the number of steps. It can be
 used in conjunction with 'Smooth'.
     A palette editor is now provided so that users can alter or create a palette to their own taste.
 The edited palette can be saved as a Fractint type .map file. Any .map files can be loaded.

    

Genfract 2.0
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    The revision 2.0  created the ability to combine the partial Mandelbrots for the critical values
 into a single complete Mandelbrot map.
  This is accessed from ' Parameters / Initial Z value '  in the menu.  These maps are resumable - so you
 can look at the Julia for a point that catches your eye and return to finish the map.
  The maps are available with three different colouring schemes. When completed, you can quickly
 re-draw it with either of the other colouring schemes by returning to ' Parameters / Initial Z value '.
 Information about the number and periods of the attractors is now given when you click on a completed
 ordinary Mandelbrot or anytime on a map.
 
  A bug in cubicb when using individual critical values was corrected 29 Mar 2002.

    The revision 1.1 re-instated the ability to colour a Mandelbrot exterior using any number of palette
 sections when the interior is black.This ability was lost in a previous re-shuffle of code.