“Fractalizing” Shapes

Hi!

I understand, maybe incorrectly, that a fractal image is (1) a set of numbers, generated by a formula, and displayed as POINTS, and (2) rules for coloring the POINTS.

In UF, is there a way for replacing the POINTS with SHAPES (e.g., a triangle)?

If so, how do I do it?

Thank you!

Dr. T

I think "points" refers to how the value of each pixel is determined and coloured (by the formula and colouring respectively). If that is correct then I think the answer to your question is no.

If by "shapes" you mean a set of similar shapes that iterate in a fractally generated manner (i.e. different size copies as generated by the formula being used) then you probably need one of the many "orbit trap" style of colourings. Look up "Orbit Traps" in the Help file for more info.

Here is a very simple example of an "Astroid" (star-like/cross) trap shape made with a Julia formula and Orbit Traps (UF3) colouring. The iterations (copies) vary in size and are arranged in a regular and orderly fashion as dictated by the Julia formula. The stars themselves are created by the colouring:

Many different trap shapes are possible. Most of these orbit trap style of formulas offer a choice of set shapes that you can further distort/manipulate through various functions and parameter settings. More advanced techniques can involve devising more unusual multi-trap shapes through the use of plugins.

I'm not sure if this answers your question.

Params for the above so you can look at the construction... look at the Trap Shape colouring parameters to see how the "shapes" can be changed:

Fractal2 {
::vpiE7hn2Ni5yutuNQY49BIvDCeVLO94INjlv0CuI5A0FFooLa3XwIRLzGdrk0JH3n+OUyymy
  iUOel1P5Mkcmhzng2r4ZGe5P/4DRRGppUwW8r9SwioPk5mDsdJbiOIkFHMs1JJRl8TClmlYt
  ITJylGNbx3OokajsW81nrrj+dui+/vkAPhxPBxJbX84Ddm1tMZ8Wjspmt4Fe2bFqmj15Liaa
  5ZSzJWSccUlwcoJnVds0Ib5a9jPUxbbl1F9mLqNCFLe520VrSBIdH+0XjXib3gpw6tpYaUFv
  omBL3sKe1OcTEvugOXAscNsezjPsvRRum35sK+3lWvlSLbrQldQk9GrZ/+o9ySRNviCH/phX
  nzV5LPuvaREt4qTsF/2xSJfh1Dt/tWIyZ0OY3utbhniXuZ9akkbb+gcMJQ//Vuss5ohlIS2+
  4DyatMX0HyV8a9eae1N1iIdTpMntC2sFSShdxP+AZ005WSxZuKSJaFcDZ5F72ueDA4WwZ3nX
  9P4yjZld71zber2X/D1rSzfp4t6F0GU8d60bqayFsX5aZGJZsj9Olqt5KMOu/waVNnaFssyG
  tQbOLl1U2oY5UNAvOT4Ku/lKtwwWYFieexVvMMa3iWT5EepdkDKh+QTZOlghUb01e26dfdzV
  r5ll2EH3WJR1f0jRXfexw23QFikjiP/cXqOhe+qf0vJb7kusrOWT5pzPl8RXd/+j1ZsnvaE4
  I/yZN0R7bn1qEqCqsFYLqk1/wz/0L/oz5fYQ+rabOckImwe+GFg9lJ2i4llfQZF7L3oky+2V
  DT0H4UyjrNqGZ+goooQLa59RPWylghdAqWTrpYYqjTObefFON0loF/dRlUpaU6uCaHTKUy8u
  MdukX0U3nrtDsXJ+3ji6sTJuLMvqlyvHzFdqO+p9AXTiXTYXdA41BALeqDAXH0Kouda2qrKG
  bms7cvaktHord0J3wWledydia5/JcX+ex3EfQ3cG5CuuVkZcnKFQoGeC1oD1g4t7eZNdj0Q3
  Wpob9I30PC16yebL+prhHOF0H7Erk/J2lh45XKMG61+kr59iVNvLcKcTyVy9j8nNONedJFtR
  06eO7CR388wcctsrVn2yIqLcnf/Ae3m9D13731COFbLdcl7Jrp26KlMz3S1Zo/lqboug3b8S
  hMvRn10KumM7bLeTDcHHMMjWq5XG5hx1HnHrRbuMojt2LaFDTyJhQtWJGwrliR9NtyH1Cu2a
  RjyM2gzi2eomTkl9HsxW7OHlougeDBnd7oJcJ4HyDXjm3u9oiQhayOvTdSE6yAGehgJrqoXK
  hbElnGbcf4nANMFdFk2b0LBocG/6Vix25b9eVy1jaCRbhL3svZPfbF4gmlG5pWfYFPPU6tm1
  pjbG5vG68YvOij9z5XBZ0U1lUl5kAbnqDDg2SxxJ3Oh+jCG7xWRp49eTxJrmnqWonD12IrHe
  FCIEFCuQhG1NGuhCte0vNXQ1BZSQImE4lJBhYSwEmE4lJBOMJPOwlJBTYSQAmE4jJB+YSQIm
  EMhJB+YSQAmEEkJBBYSwUmE4lJBeYSgSQNIomhyuyE3CZYS7EwLrCuwqcs9Muy5xbYVwAryt
  K2BXdd/5nVBhZVgfWFMDrCmjVBhZVw8sK4usKYGWFcHWFEgVB+ZVQQWF8JYVjnz7clsbR35e
  NNENLkXmkhCQz8cGGAaO6jpZjtxPQzZCepZj9hn7TTpZgDN7mtwk2CeoZw80MIANDCRzA/0M
  wDND8Szg7Rzgw0MYGaGMDNDnSzwQ0M0PND/U0MMMNDDRzQv0MMENDnQzQv0MMENDnQzwJ0MM
  AND9RzQf0MMENDnU2i+oZYAaGGkmhBoZ4UaG6lmheoZYYaGOhmhepZoHaGOmmhTpZ4UaG6hm
  hhoZYYaG6nmhzQzw5oZYYaGOPNDvLNDnhmh3hmhBoZofaGGkmhfCaGeXaG+JoZ4s0M8u0MMA
  NDnhmh3jmh3nmh+oZoHaG6lmh+oZoHaGOPNDDQzwQ0M0PND9QzQv0M8e0MMMNDnhmheoZF2a
  OKp39xmpLKvJyZnE6IdVTDVIZ/rsOX8dWcU/3jNZ9mNbgk0zy4udnHw+hr7/e+d+yjDG+c/Q
  qr1OqP+w/HBB4xE=
}

Dear Chris,

Thank you for your reply.

Yes, when displayed as an image, a point is a pixel that has a value generated by the formula. The coloring rules (a combo of the Coloring Algorithm and the Gradient in UF) assign a color to each value.

You did answer my question. I am trying to do something very similar to your Astroid example. Use a Fractal Formula such as the Julia Set and a Coloring Algorithm such as the Orbit Traps that you suggested. I’ll look at Orbit Traps.

However, my ultimate goal is to use a shape such as a Golden Spiral (a common geometric shape), which may or may not be available in the Orbit Traps. And, as of now, plugins are “beyond my pay grade.”

I wonder if is possible to create a layer with the image of the shape (e.g., a Golden Spiral) and then, somehow, use the image as input to the Coloring Algorithm.

Dr. T

Ah, well this is where plugins show their versatility! Using plugins it is possible to devise a spiral trap shape (though not necessarily a golden spiral) which could be deployed in the same way as the astroid shapes above.

Your other idea, of using an image and mapping that onto a fractal in an iterated way is also possible using an "Image trap plugin". This, however, can be a wee bit tricky so again I would say it is a rather more advanced procedure but it IS possible.

Here is an example of an outside image, a clock face, applied to an orbit trap arrangement in one of my images: LINK

I regularly use various textures from imported images to texture trap shapes in my work too. So there are a lot of creative possibilities with these techniques.

Dear Chris,

Again, thank you for your reply.

The link didn't work. Can you post the link?

Dr. T

Oh sorry, I should have checked it.

https://www.deviantart.com/velvet--glove/art/Spring-Time-285951406

...hmmm. That looks "live" but isn't. You'll have to copy/paste it, I think.

Dear Chris,

Thank you for your reply.

Yers!!! That's exactly what I want to do. Now I have to figure how to do it.

Dr. T

Ron Barnett has a series of very thorough tutorials on the use of plugins here:
http://www.hiddendimension.com/Challenges/UF5Challenges.html

They are intense but informative and will give you all the information you need to make a start with this method of creating fractals. You need to start at the beginning and work your way through the list in order. Number 9 covers image import.

Given time to properly study and practice this material you should be able to figure this out. It took me several months to get a real handle on all this but it is intensely rewarding when you start to understand it.

Dear Chris,

One more time, thank you for your reply.

I'll work through the tutorials.

By the way, in the first tutorial, I saw a UPR script. How do I paste it to UL?

Dr. T

Just select & copy the whole block of text from the starting title: Fractal1 all the way down to and including the final curly brace at the end: }

Then open a new fractal window in UF or click on an already open one and paste. UF should then present you with the image.

Similarly if ever you want to share your params:

• click on your fractal image window
• Ctrl-C to Copy
• go to your forum post/email/reply window/Facebook or whatever and Ctl-V to Paste the text there.
• On this forum there is a toolbar command for pasting a code block (the page icon with <> on it). That's what I use for pasting parameters here.