Mar / Apr 2016 Lite Challenge: Compass

[Deadshade]

Fractal art is infinitely (literally) more difficult than handrawing because it is like looking for a needle in a billion of haystacks.
Also fractals behave as a whole so that if one slightly changes one part, other parts change too what makes fine editing almost impossible.
However whan one got the taste of the hunt after the ultimate fractal, it is hard to resist .
I am sure that somewhere in the infinite parameter space there is the mother of all compasses and I'd like to have a look.

Yet as it is practically impossible to go for a very definite shape and color, I will not be able to go for the usual WIP system. So I'll publish some of the best results I'll find in the form of raw fractals and decide with help of your suggestions for the one that I'll keep for post editing as the final entry.
The first one I found is a Clockwork compass beautifully consistent with a sci fi or a middle age style map.

Compas1.png

[Nidhöggr]

I like the idea behind this, and this first result looks very steam punky to me. One could beautifully flesh this one out.

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[Josiah VE]

That is utterly cool..

By the way you forgot to put your title as "Mar / Apr 2016 Lite Challenge: << your title here >>"

[Lingon]

Yeah, like Josiah said, I think you'll need to format the title like that for the thumb scraper to pick upp your image, when you decide to add the Latest WIP tag. What you have there looks absolutely awesome though!
As someone who knows nothing at all about fractals (except that they are mesmerizingly beautiful), I'm curious about how one actually does it. Don't need a full tutorial or such, but it'd be fun if you felt like sharing some details of the process

[Deadshade]

As someone who knows nothing at all about fractals (except that they are mesmerizingly beautiful), I'm curious about how one actually does it. Don't need a full tutorial or such, but it'd be fun if you felt like sharing some details of the process

It is good that you don't ask for a full tutorial bacause there cannot be one
The principle of fractals is deceivingly simple.

A fractal is a mathematical structure always based on iterating a function.
A very simple example is the Koch flake.
This picture shows how it is constructed starting with an equilateral triangle where one removes the middle third of each side and puts a smaller equilateral triangle on the place.
Then one does the same thing to all sides again and so on to infinity.
The result, the Koch flake, is an example of a closed curve that surrounds a finite area but whose length is infinite.

Koch flake.gif

Perhaps the most famous fractal is the Mandelbrot set whose definition is also simple.
You simply take all points P of a plane of coordinates (x,y) and verify whether the iteration
Z(n+1) = [Z(n)]² + C stays bounded.
Here Z(0)=0 and C is the complex number x+i.y defined by the point P you have chosen.
If for a given C the iteration is bounded, you color the initial point in black and if not you don't.
The result of all the black points is not a meaningless chaos but a stunning shape of infinite complexity.
This picture shows a part of the Mandelbrot fractal. Recall that if a point is colored, it means that the iterated function stayed bounded for that point.
Mandelbrot.jpg

Now if you generalize this principle by taking any function or a set of them and iterate it, you obtain an algorithm which will create a fractal for some values of the functions' parameters. However it will create garbage or nothing for most values of parameters.
Fractal art is done by using such algorithms and free software like Apophysis or Jwildfire is available to run them.

Now what is done in practice ?
Let's just look at the infinite complexity.
You have something like 100 different functions (sin, circle, hyperbole etc).
You may combine any number of them to produce a given fractal.
Suppose you would try only combinations of 2 functions – there are 10 000 combinations.
Most functions depend on parameters – you may have 3 of them in average and each may take 100 values (actually much more but we look here only at the principles).
That makes 100^3 = 1 000 000 possible combinations of parameters.
So finally if you wanted to explore all possible fractals created with only 2 functions depending each on 3 parameters which may take only 100 values each , you are looking at 10 billions of tries.
This is clearly impossible.

And as it is also impossible to predict , mathematically or otherwise, what combination out of the 10 billions of possibilities will give you the mother of all fractals, the only way to do is experience.
I would compare it to collecting mushrooms – some persons would walk hours through a forest and find no mushrooms and some persons have an idea where the mushroom rich corners are and bring a basket full of them in 20 minutes.
Fractal art is developping the intuition and skills to find those mushroom rich corners. Basically the process is that - I have a notebook where I write what kind of effects I noticed when using this or that function and this or that corner of the parameter space.
It takes time and much learning but the reward is that what you find will always be unique – nobody else has ever seen your fractal before and nobody will be able to redo it unless you tell him where you found it.
And there is also the advantage that if one has the patience and skills, no knowledge of mathematics is needed whatsoever. So basically anybody can try it and as they say, "Beati Pauperes Spiritu"

[Deadshade]

Btw just to illustrate the unpredictability.
5 minutes ago I was in a corner where I thought some compasses might be hiding and here is what I found instead.
It is a quite nice surprise but it is not a compass

Starfish.png

[ChickPea]

Ha, that's amazing!

[Nidhöggr]

What Software did you use?

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[Bogie]

Wow, that one almost looks like a real starfish!

[Lingon]

That's very… maths Thanks for the explanation, didn't understand most of it but it was interesting anyway So in practice, if I didn't get this completely messed up in my head, what you do is that you write a function, and a program then draws a visual representation of the function, and you surf around the infinite image looking for cool parts of it, and with experience you also learn how to change the function to get desired changes to the image? Somewhat right? And the results can be exported as a raster image for PS/Gimp/etc editing, I guess?
(and of course, there cannot be a FULL tutorial in any art medium, but you understood what I meant )