Mar / Apr 2016 Lite Challenge: Compass

[Josiah VE]

Staaarfiiish!!! THat looks really cool.

[Deadshade]

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?

Somewhat.
But you don't write functions - you select them in a table that is in the software. Some of them are usual functions like logarithm or cosinus and some of them are specifically created like Bwraps or Lazysusan (yes that's a name of a function).
So you pick 2, 3 or whatever number of functions you want. Then if the function depends on some parameters (like Cos(a.x) depends on parameter a) you put in some numbers for the parameters. There are a few more transformation that you can add on top like : scale, translate, rotate.
Then you are done so you launch the iteration and obtain either a black screen (there was no fractal where you tried), or a pixel mess (there is a fractal but it looks like Nothing) or the grail - a sharp nicely colored fractal.
In this latter case you can try all kinds of transformations on it. Slightly change the parameters to see how it deforms, zoom on a part, change colors, add another function to see what it does etc.
If the former, you must remember that it can't be excluded that you obtained a black screen or a pixel mess with a parameter at 1.3456 but there can be a beautiful fractal hiding just around the corner if you only change the parameter to 1.35.
You can never know and it is here that experience and skills play a role.
And of course you can then export the result as jpg or png to Gimp and do some maginal editing (mostly the background only).
Generally you can't edit much because a fractal is a structure of a multitude of ultrafine details and color gradients so that using Gimp on it is like trying to improve a cobweb with a sledge Hammer.

Wow, that one almost looks like a real starfish!

Yes but if you count, you'll notice that it has 7 tentacles what is impossible

What Software did you use?

I have several softwares but what is here is done with Apophysis 7X.

[Robbie]

I've always been awed by Fractal artwork. I use some fractal functions in some of the 3d work I do for work, and lets not forget a lot of fractal math goes into some of the world generation software used here...but this...this is really cool to me when you are able to dig down deep into the mathematical underlyings of what appears to be organic and random, but is instead quite deeply ordered and logical. There's so much in our world that we see that shows evidence of mathematical design. I love it! I can't wait to see what you're able to dig up!

[Deadshade]

Here another quite different style that I managed to find. Recall that these are raw fractals with no fine tuning so far - I am just hunting.

Compassy.png

I would really appreciate if you could tell me what is for you the essence of the "compassness". Sofar my hunt is relatively unfocussed. I look for pointed ends (preferably 8 ), for circles or polygons in the center and eventually for small subdivisions on the border like in the clowkwork compass. Also basically only 1 or 2 colors (here it is the handdrawing influence).
What is the part of a compass (graphically) that is most important for you ?

[Robbie]

I would say at least 4 points, 8 preferred...unfortunately, mathematics wise, I don't see how this could be done, but I always think the larger North direction usually makes a difference also.

If you could find something with the 4 major, and then the 8 minor and 16 minor-minor, that'd be real cool, but thats probably a pretty tall order. I liek the most recent you just posted more than the first one you posted though! It's pointier.

[Deadshade]

If you could find something with the 4 major, and then the 8 minor and 16 minor-minor, that'd be real cool, but thats probably a pretty tall order. .

I am convinced that everything that can be imagined, has been imagined and will be imagined already exists somewhere in the infinite fractal space.

Your order was interesting and difficult so I took it up (if I understood well what you meant).
The difficulty is that when one respects the requirement for 16 regularrily spaced directions it asks for circular symmetry. However that leads to a circular symmetry for scales too. It is not so difficult to respect either 16 directions OR directions of inequal length but it is very hard to respect both.
But here is what I did and it respects your 4 major, 8 minor and 16 minor-minor. Of course after all these constraints I imposed, I had little control over the detailed shapes so it gave this fractal :

compassz.png

[Robbie]

Very cool! Thumbs up for sure!

[Nidhöggr]

Apophysis is really awesome, Thanks for the tip! You stole my freetime and propelled my electricity bills skywards! I'll send you the invoice.
As for your last render: I certainly like the general shape of it, I think altering the colour theme could help to make it asthetically more pleasing. As it is now, it lacks some contrast, in my opinion.

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[Deadshade]

I think altering the colour theme could help to make it asthetically more pleasing. As it is now, it lacks some contrast, in my opinion.

Better ?

compassz.png

I then continued with Robbie's requirements for symmetric/assymetric points.
It gave this which would suit a sophisticated fantasy map . I invite you to zoom at it - you will notice magnificent very fine golden threads woven in it.

Compaswhite1.png

Not far from the previous compass was the following fractal.
It has many features of "compassness" even if it is not really a compass so I post it just for the eyes' pleasure .

Midgard.png

[Josiah VE]

Love the second one because it actually looks like a compass rose, looks amazing..