Chaotic Attractors Tutorial

These, often called Strange Attractors, are iterative systems that don’t seem to go anywhere, but do (approximately) repeat. Unlike most of the formulas in UltraFractal (UF), the iterations don’t diverge to infinity or converge to a point.

A simple example is the Clifford Attractor, named after Clifford Pickover, as in Layer #1 of the upr file at th

Perturbation-style formulas depend on the #dz value remaining small enough

for fixed-point arithmetic. I managed to sabotage myself by setting a high

bailout value of 1e20 on this deep zoom with perturbation.

After reducing the bailout to 1e10 the formula worked beautifully.

(I wanted a high bailout because I was using smooth coloring)

Disturbation_bad {

fractal:

title

Hi, this is my first topic here and I want to know how do I make matrices in Ultra Fractal.

Thanks!

Phillip
posted Feb 4 '22 at 10:46 am
Hello,

since some people were wondering how I made some of my images, I decided to write a short tutorial on how to use the coupling loops formula in phs.ufm which I used several times over the last months.

When you first open it, this is what it looks like. The loopy stuff is located in the valleys of the main set and also the minibrots. As a rule of thumb, the higher c is, the stronger

(Literary readers: yes, this is a reference to the Wallace Stevens poem, “Thirteen Ways of Looking at a Blackbird.”)

This image has 16 fractals arranged in a 4 by 4 array. All 16 have the same gradient and the same Formula tab (Julia from Standard.ufm). All of the Outside tabs use Plug-in Coloring (Gradient) from Standard.ucl, and the Distance Coloring plug-in from jlb.ulb. The di

I have updated my Distance Coloring plug-in (in jlb.ulb) in several ways.

New distance plug-ins:

Gaussian Integer, similar to the coloring in Standard.ucl. This often gives interesting results when used only on early iterations.

Triangle, like Circles or Square, color according to whether z is inside or outside.

Modified plugin:

Exponential Smoothing, with addition

Hello, i'm a uf6 apprentice and I have a question.

I'm testing and studying Kerry Michell tutorials

As you can see, my image is not as perfect as the image obtained http://www.kerrymitchellart.com/tutorials/basket/basket.html

I have made a copy and pasted of the upr of kerry and I have rendered, then I have compared both images and mine imge has defects. because?

you can

I have uploaded new Distance Coloring plug-in files to jlb.ulb. These are similar in concept to Orbit Traps: for each iteration, as the z associated with a pixel moves in the complex plane, information can be accumulated about distances. Afterwards this information is used to calculate an index into the gradient for coloring. See a sample image and a upr in the following post.

Load the upr in

Now two examples with just two layers, a top layer for the lines and a bottom layer to color the cells. Here’s one with 200 rectangles. Because cells are colored with index equal to n/Nmax, shuffling the colors often gives a more pleasing result.

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200Rectangles {

::fPzc0hn2tT1yutNMQw7Gw/DE6udkYEtiTBPU72EgAHggkDJ9UAj0KLmQRKQRna/33VP8jaJn

2zt5m0s7O7SyZ

Years ago, rkb.ulb included code that allowed the making of Mondrian-type images, but it is no longer in that file. I thought about this for a long time and decided to develop such code, though mine is totally different. (The rkb code used Trap Shape, and mine is entirely in the outside coloring.) Here’s an example of the result. Not as good as Mondrian’s, but reminiscent. And not at

I've been a longtime user of Photoshop and other graphics applications, but not spent much time creating fractals. I've looked at hundreds of fractals and there is one style in particular I really like and would be happy to create in a variety of ways. I think it's referred to as chaotic bundle or chaotic thread, but I may be mistaken regarding this. What I need help with is the steps in UF to cr

Switching the order of the two formulas, changing the parameters a bit, and switching to Mandelbrot mode, gives a fractal with some convergent and some divergent areas.

C-P'-M-M {

::Yqouqjn2VaZzuNKMQA47RKvDIusnIgNhQSX5Lta3DVbXVps3jcwDg3asRGnmm3+1GSSb2km4

yJwz38jnZsZK10CDVc34RBBGuRAkwHie+bRPF9UYwWOzUTmnkEUD8qaDZm9VBdHo7IInGFag

xNdkwH5NB3L2AffeMCHjTQLCHPqns3yF0WDXJJh3TLepSr2IZhBqWaB3sjgsGtB

The second type of plug-in is “Combo.” It allows combinations such as (f1+f2)/f3 or f1(f2)). The latter means evaluate f2 to get a new value, then use that value as input to f1. The following example starts with Perlin 3D noise, followed by repeats of a Combo of Mandelbrot, Mandelbar, and Function.

D-N-CMM'F-J {

::q3UZWin2deVwutNOQ07Gw/DC6y2uLstIVkVdXwLJF5QQTxCk90iFwgiiyibpIVpoTq7

The available formulas, all in jlb.ulb, are listed below. All of them have parameters that can be changed and hints that describe the options.

Do nothing (a placeholder to be used if no formula is desired)

Divergent formulas (usually)

Mandelbrot

Mandelbar

Function

Power

Polynomial

Gnarl

Gnarly

Perlin 3D Noise

Convergent formulas

I have just uploaded Simple Switch Formula to jlb.ufm. By default it calls my SwitchCombo plugin in the new library, jlb.ulb. This allows generating new combinations of formulas; all of them allow switching from Mandelbrot-type mode to Julia-type mode or vice versa with the F7 key or pressing the Switch Mode icon on the toobar. Both divergent and convergent formulas, or some of each, can be used.

DoctorT
posted Jan 2 '19 at 10:26 am
Hi!

More about plugins …

I’ve been doing some readings about plugins and this is my interpretation of what I’ve read.

In the computer world, a plugin is a program that adds functionality to a larger program. In the context of UF, plugins add functionality to UF but are customized for particular formulas, algorithms, or transformations.

Thus, it follows that one

DoctorT
posted Jan 1 '19 at 1:22 pm
Hi!

To create a fractal image one could understand the relevant math (i.e., Fractal Geometry) and the functionality of the software that generates the image. The relevant math is beyond the grasp of most artists and the functionality of complex software such as Ultra Fractal is, at least initially, also beyond the grasp of most artists.

As an alternative, one could ignore the math and id

DoctorT
posted Dec 30 '18 at 2:18 pm
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

DoctorT
posted Dec 30 '18 at 5:40 am
Hi!

I want to create a JPG file for printing on canvas. The canvas size is 16 inches (W) by 12 inches (H). At 600 PPI, the JPG file is 9.600 pixels (W) by 7.200 pixels (H).

To begin a fractal, what parameters should I use in the “Fractal Properties: Image”?

Or, does it matter? If UF files are scalable like SVG files, then only the width/height proportions matter.

Th

DoctorT
posted Dec 29 '18 at 10:28 am
Hi!

I am posting this query as an image to bypass the Spam Checker, which keeps rejecting it.

Thank you!

Dr. T