Forum: Fractals


Subject: Apo is taking over the world

Deagol opened this issue on Apr 24, 2006 · 45 posts


JoelFaber posted Sun, 30 April 2006 at 1:11 AM

Quote - I can't figure out what the 'final transform' button does either, and there is still no documentation!  I tried tried the mailing list, but I don't understand half of what they are talking about, they are like gearheads and I'm a Sunday driver, LOL.  I also would like to know how to evenly shrink the entire triangle, rather than scale it so that it remains oriented around a single angle.  I have tried using the tiling script, but it doesn't seem to do much for me.  I have only gotten one image that was tiled, and it was kind of boring.  Any help would be good.  Tutorials would be amazing!

Thanks,

~Vivian

Oh, perhaps she meant presumptuous or impertinent or impudent or insolent.....not that I think Rykk is any of those at all!

Each transform (a triangle in the editor) maps one coordinate space into another coordinate space.  This just means that every point (x1,y1) gets transformed into another point (x2,y2).  The flame fractal algorithm randomly transforms points from one coordinate space into another repeatedly (or recursively, if you will). To get a better understanding, try this:
 -  Start with a flame you like.  Something simple with fine lines would be easiest.  Make sure it doesn't have a final  tranform (final xform, for short)
 -  Add a new transformation in the editor.  This new transformation might make some changes in the colouring, but it doesn't change the shape of the flame.  This is because a linear transformation at the default size and position doesn't change the coordinate space.  Mathmatically,  (x1,y1) = (x2, y2).
 - Now try rotating the new linear transform a little bit.  Notice the effect that this has on the flame.  The flame has been rotated and superimposed on itself repeatedly.  There are many copies rotated at multiples of the angle that you rotated your linear transform because of the recursiveness that I mentioned above.
 - Delete that linear transform and add a new final xform.  This should be a linear transform with the default size and position.  Notice again, that this doesn't have any effect on the shape of the flame.
 -  Try rotating the final xform by a few degrees.  Notice this has a different effect than rotating the first linear transformation.  The whole flame rotates because the last mapping (or "final transform") is one that rotates every point in your flame a few degrees.  There is no recursion in this case.  The whole flame is mapped into a new coordinate space.

I hope this helps.  If something doesn't make sense or whatever, just send me a message.  I'd be more than happy to help out.  btw Vivian, your post was hard to read.  A different colour would be better :)

~~

As for the original discussion, I think the best fractal images, whether they were made with Apophysis, UltraFractal, XD or whatever, are absolutely beautiful!  The rest I'm tired of seeing.  I don't like random flame fractals and I don't like that many UF images look like the same spiral with different colours. 

Producing art isn't easy.  Producing colourful pictures is.  I haven't played with UF much, but I believe that much time must be spent learning how to use different colouring techniques and formulas.  I think one of the things that holds many Apophysis users back from making better art is that it is far too easy to create random flames.  Take a look at Nick's (grinagog), Andrew's (psion005) and Michael's (MichaelFaber) and my galleries.  There is nothing random there.  Those artists took time to learn how to use the different variations to get a desired outcome. When I make tiled fractals, I often use a pencil, paper and a scientific calculator to help me out with the trigonometry that I need to get everything to line up properly.  I know that is a little extreme, but using the editor and learning how the different variations behave when they are manipulated is the first step Apo users can make to becoming better artists.

Sorry for writing a very long post :)

All the best,
Joel