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in this post I  will discuss the creation of free transform fractals, how they are relevant to the fractal community, why they are fractals, how to build them with only open source software, i will also deeply discuss the theory behind them  (please note I am not a mathematician  but I will do my best to follow geometry conventions)    O0

A free transform fractal is a fractal created by manual iteration on a graphics program like inkscape, photoshop, illustrator ...ect.
The idea works like this, let's say we have a image, now we will copy that image modify it and attach it to the original image,
now we do it again.   OK than  we  copy the entire collage of images and attach at various points.

see images for example

please note, some creativity was used in the placement of the copies that is the fun part.

These collage fractals can get very big, and if done right very symmetrical (i will get into symmetry later)    

    

while on the web I came across a fractal type called collage theorem

for some information on it check this link out
http://scimath.unl.edu/MIM/files/MATExamFiles/Snyder_MAT_Exam_ExpositoryPaper.pdf (http://scimath.unl.edu/MIM/files/MATExamFiles/Snyder_MAT_Exam_ExpositoryPaper.pdf)

this idea influenced my art (mostly by looking at the pictures because as i told you I am by no means a mathematician)

 O0   

during my first year as an artist I used photoshop (at the time i did not know about the conspiricy of d.r.m.  http://www.defectivebydesign.org/ (http://www.defectivebydesign.org/)  )

but any i learned a lot from the the website hear  http://podcollective.com/fora/viewtopic.php?t=579 (http://podcollective.com/fora/viewtopic.php?t=579)

this website was my inspiration and the fractals i make are a heavily modified version of this idea

I later learned by combining the power of inkcape  and gimp I could make a program better than photoshop 

this is easy to do in inkscape  there is an extension to extract or embed images so you can edit them externaly

please note after editing an extracted image you must embed it or else wen you edit it again it will affect the entire fractal not just the tile you are editing   

while making a fractal collage your images should be in bitmap form  fractals of large size should be built in modules each module should be converted to a bitmap this greatly reduces memory usage for instance a fractal is first  built when it gets big it is rasterized  the raster image is far less memory heavy on inkscape you should use the page size to limit the size and scale anything to to fit within this before rasterizing  if you do this inkscape won't hang  i set inkscape to rasterize at 200 dpi  i suggest you do this to

to recap workflow is like this

build fractal
rasterize
use that as next iteration
rasterize
use that as next iteration

you can reuse part's by saving them as bitmaps to import (fractal seeds)

when aiming for symmetry this becomes ever more important due to the fact that reflecting a single tile requires moving all tiles so the image is oriented for the reflection

see example below   

even with all these wonderful tool your fractals most likely wont be perfectly symmetrical that is why you should build them in modules so you can use gimp to cut them in half and delete one half   than duplicate the half that is left with inscape  

note the symmetry in the bottom image

during your work you may need to cut blur or do other things to tiles

to do this you must have gimp installed and have it set as inkscapes default image editor

during this demo i am going to cut a tessellation slot in my fractal

first i will select it in inkscape than i will go to the extentions menu/images/ extract or embed

i will hit extract just hit ok to all the directory diarrhea (lol) it's just a swap file you don't really need to know where it is (it's in your home folder)

after extracting  the image select it right click on it you should see a new option there (edit externally) click this it should open the image in gimp were you can preform bitmap operations on it after editing the image save it in gimp and exit gimp the image should now update

ok your almost done now go back to the menue  extensions/images/extract or embed this time hit embed and   just hit ok to all the directory diarrhea
good if you did that your image is now back inside inkscape

see image below

I love feedback just don't be mean of post anything negative i will be happy to go over anything again or give people links or examples and answer questions the best I can one thing though don't like tell me they aren't fractals there a form of natural fractal made by people I put my heart into these things

Great Stuff here!

I hope you don't mind me moving it to a more appropriate home   :D

i don't mind as long as people see it thanks by the way

In addition to gimp, there is paint.net (freeware) for windows users.

  It has loads of plugins, some of which would be very useful for your free transform fractals.  The various mirroring/distortion/duplication plugins allow one to do similar things to what you've posted above.

Thank you so much for this and your link: http://podcollective.com/fora/viewtopic.php?t=579 (http://podcollective.com/fora/viewtopic.php?t=579)!
I created this.  For so much more fun I will now make a series of these. YEAH!  Cheers.
 (http://www.fractalforums.com/gallery/3/2367_13_09_10_2_08_47.png)

I appreciate "artwork" that has self-similar and repeating patterns, and there are many examples all through history (several have been referenced in various topics of this Forum).

Though I understand the basics of what you are doing, and the references you have given, I am not sure as to whether I would consider the process as being truly fractal in the strictest and/or mathematical definition.

It probably would have helped others in reading your "monologue" to have included punctuation.  I found it difficult at times to know where a sentence stopped and another began.  Or when a phrase should have been separated from the rest of the sentence with commas.  (The misspelled words I was able to get around and understand your intention.)    ;D


I am very blunt in my responses.  You can take it as being mean or negative if you so desire to categorize them as such.  But this is not a social network where people should come looking for pats on the back and nothing but praise (try the UF-List, Renderosity, or other such places for that).

And I surely hope you did not intend to be telling me what I should or should not say to you or anybody else!!!
 

Here's another one using this method.

(http://th09.deviantart.net/fs71/PRE/i/2010/255/a/7/fern_of_ice_by_thunder_wave-d2ym1lc.jpg) (http://th09.deviantart.net/fs71/PRE/i/2010/255/a/7/fern_of_ice_by_thunder_wave-d2ym1lc.jpg)

And here's another one!
(http://www.fractalforums.com/gallery/3/2367_13_09_10_4_02_42.jpeg)

Okay, I am obsessed!

I made one for ice, earth, but now I must make one for fire.  It reminds me of anime.
Now I need one for air, water, space, time, etc.....
(http://fc09.deviantart.net/fs71/f/2010/255/6/5/burning_down_the_house____by_thunder_wave-d2ymbt4.jpg)

the purpose of this artform was not to be pure fractal. it was to let people have more control over fractals so they could be more artistic therefore they are sort of hybrids between fractal and photomontoge.

and by the way sorry about the punctuation I will fix it when i talk i get so excited I forget. 

very nice fractal.  do keep in mind however that there is pretty much unlimited ways to do this. you can make trees, ferns, spirals, gaskets, millifiori  beads (virtual ones) and many other things you don't have to follow the directions exactly that is the fun part. I can't wait to see how you develop as a new artist.   O0 ;D by the way just curious what license is your art I make my stuff public domain so people can use it as fractal seeds (just my personal choice) 

OK clearly I did something right because you mastered this pretty well.

Thanks Matty!  I love this idea!  I'll have more later.

Oh, I don't really know where to put my art in what domain.  I guess it's free to use as long as I am credited and thank you for the complement!
Here's my latest:
(http://www.fractalforums.com/gallery/3/2367_13_09_10_5_08_18.jpeg)

yup that's called a creative commons license you must credit the maker

sorry I may have confused you with why this is important but these fractals can involve lots of reusing art and that can be a fun way for too artists to have an art conversation  by me making things public-domain it  means it no-longer belongs to me but to the entire human society i would not advise doing this if you aren't OK with other people selling your work (they can't copyright it however so you could still sell it) but yeah any way I use public domain because of my religious beliefs   

 the background was made to look like a cake on gimp  four roses were placed than I assembled modules  from the roses in a separate inkscape file  when the modules were complete i placed them into the first image and tiled them into place  


the first image is the fractal

the second image is one of the modules

this fractal is my best example of how you can achieve near perfection by trying hard enough even without formulas

I admire your work. :)

It's not that hard you just have to plan everything out, grow the appropriate modules to grow the modules you need after you have built those put them together the modules must begin to converge around your idea also key-framing (re-saving as you go under a list of names) helps a ton as it allows for time travel so you can fix mistakes