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ThoughtWeaver
Logan Apple
Artist | Hobbyist | Digital Art
United States
I'm a computer science major at Caltech who enjoys archery, sword-fighting, designing fractal art, programming, and learning in general.
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Foci-Linear Nebula Tutorial

Sat Nov 17, 2018, 11:00 AM by ThoughtWeaver:iconthoughtweaver:
:iconprojecteducate:
:iconprojecteducate:


Fractal Art Weekend



Hello there!

My name is ThoughtWeaver, and one of my favorite styles of fractal art is foci-linear nebulae. There are numerous ways to create fractal nebulae -- this is just one of them -- so I hope you'll take the time to learn and explore what other possibilities are out there!

This tutorial will be using Chaotica, which you can acquire for free here: www.chaoticafractals.com/

Note that this tutorial is moderately difficult. If you have no experience creating fractals, I recommend starting out with beginner tutorials, such as the fantastic ones created by C-91 and tatasz.

Also note that I tend to use a coordinate abbreviation (x, y) to imply that you should set the x-angle to x and the y-angle to y, or the x-coordinate to x and the y-coordinate to y depending on the circumstance.

Without further ado, let's get started. We'll be designing the fractal depicted below:

Screen Shot 2018-11-03 at 10.38.19 PM by ThoughtWeaver

Setup


To get started, set your window size to something relatively small, such as 640x384. This will make it easier to see what's happening to the fractal as you design it. We'll be using the world editor extensively, but don't worry there are instructions on how to get to most elements of the editor as the tutorial progresses.

Now, open up the world editor (from Window->World Editor at the top) and let's get started!

Iterators and Transforms


Iterator 1

Add in a new iterator that will serve as the base of the fractal. The standard transformation to have on this iterator for fractal nebulae is spherical and foci-linear nebulae don't deviate from that, so add in a new transformation and set it to Spherical with a value of 1.0.

Now, we want to adjust the iterator by changing the values of its pre-affine. Let's start by rotating it -15 degrees, taking it from (0, 90) to (-15, 75). Then, set the position to (-0.7, 0).

Screen Shot 2018-11-03 at 7.11.44 PM by ThoughtWeaver

Iterator 2

Add in a new iterator, then add in a new transformation and set it to Linear with a value of 1.0.

Now, we want to adjust the iterator by changing the values of its pre-affine. Rotate the iterator by setting its angle to (90, -180). Then, set the lengths of the iterator to (0.9, 0.9). Then, set the position to (1.4, 0.7).

Screen Shot 2018-11-03 at 7.12.51 PM by ThoughtWeaver

Iterator 3

Add in a new iterator, then add in a new transformation and set it to Foci with a value of 1.0.

Now, we want to adjust the iterator by changing the values of its pre-affine. Set the lengths of the iterator to (0.8, 0.8). Then, set the position to (-0.5, -0.5).

Screen Shot 2018-11-03 at 7.13.21 PM by ThoughtWeaver

Iterator 4

Add in a new iterator, then add in a new transformation and set it to Linear with a value of 1.1.

Now, we want to adjust the iterator by changing the values of its pre-affine. Rotate the iterator by setting its angle to (30, 120). Then, set the lengths of the iterator to (0.45, 0.45). Then, set the position to (-0.5, 0).

Screen Shot 2018-11-03 at 7.13.53 PM by ThoughtWeaver

Iterator 5

Add in a new iterator, then add in a new transformation and set it to Foci with a value of 0.9.

Now, we want to adjust the iterator by changing the values of its pre-affine. Rotate the iterator by setting its angle to (115, -155). Then, set the lengths of the iterator to (0.6, 0.7). Then, set the position to (0.7, 1.3).

Screen Shot 2018-11-03 at 10.57.47 PM by ThoughtWeaver

Iterator 6

This is the most important transform in terms of what shape you want the inside of the nebula to have, specifically the gaps in between the large hourglass-like shapes. While Fisheye is generally a good option, there are plenty of other transforms with which you could mess around. Add in a new iterator, then add in a new transformation and set it to Fisheye with a value of 1.0.

Now, we want to adjust the iterator by changing the values of its pre-affine. Rotate the iterator by setting its angle to (115, -170). Then, set the lengths of the iterator to (0.6, 0.6). Then, set the position to (1.8, 0.3).

Screen Shot 2018-11-03 at 10.58.09 PM by ThoughtWeaver

Iterator 7

Lastly, add in a new iterator and leave it entirely empty. This will create the stars of the nebula.

Screen Shot 2018-11-03 at 10.58.23 PM by ThoughtWeaver

Camera Transform

While this is technically optional, I find that using Mobius as a camera (final) transformation is particularly useful for manipulating the fractal into the position and general shape that I desire. Think of it like the standard Linear transformation for the camera with a few useful bells and whistles.

You can click the "Toggle Camera Transform" button in the world editor which will give you the option to change the camera transformation. Change it to Mobius and set the parameters to (1.8, 1.0, -0.2, 0, 0, 0.2, -0.2, 1, 0).

Xaos


As is apparent from the pictures above, we haven't quite gotten to a beautiful nebula yet. We need to alter how much each iterator affects the other iterators in order to balance out the structure of the nebula. You can find the parameters we'll be modifying in the world editor under "Iterator Selection Weights" for each iterator.

Iterator 1

Set the weights, in order, to:

Screen Shot 2018-11-04 at 12.28.40 PM by ThoughtWeaver

The weights in this iterator are primarily intended to bring out the edges of the external structure of the nebula.

Iterator 2

Set the weights, in order, to:

Screen Shot 2018-11-04 at 12.28.41 PM by ThoughtWeaver

The goal of these weights is to bring out a moderately weighted center of the nebula to avoid leaving large gaps in the overall structure.

Iterator 3

Set the weights, in order, to:

Screen Shot 2018-11-04 at 12.28.43 PM by ThoughtWeaver

The weights in this iterator are primarily intended to bring out the edges of the overall structure of the nebula.

Iterator 4

Set the weights, in order, to:

Screen Shot 2018-11-04 at 12.28.44 PM by ThoughtWeaver

The weights in this iterator are primarily intended to bring out the edges of the internal structure of the nebula.

Iterator 5

Set the weights, in order, to:

Screen Shot 2018-11-04 at 12.28.45 PM by ThoughtWeaver

The weights in this iterator are intended to manipulate the weights of color applied across the fractal, which will be an important aspect when we get to working with the shaders on each iterator.

Iterator 6

Set the weights, in order, to:

Screen Shot 2018-11-04 at 12.28.46 PM by ThoughtWeaver

The weights in this iterator are primarily intended to bring out the edges of the external structure of the nebula.

Iterator 7

Set the weights, in order, to:

Screen Shot 2018-11-04 at 12.28.47 PM by ThoughtWeaver

The weights in this iterator are intended to bring down the intensity of the stars and make the nebula itself fully visible with stars as a nice detail amid the soft underlying structure.

Gradient and Shaders


In order to arrive at the fractal depicted at the start of this tutorial, we'll need to add in a gradient and set up the palette locations and blend speeds for each iterator. You can find the parameters we'll be modifying in the world editor under "Shader" for each iterator. The gradient I designed for the final product was focused on a blend of auburn, gold, and green:

Screen Shot 2018-11-03 at 7.10.38 PM by ThoughtWeaver

In my experience, blue goes well with other vibrant colors, such as red, yellow, and green. Try to focus on compositions that use complementary colors, separated by section. I usually keep one or two colors for the foreground (the exterior edges and primary structures within the nebula) of the nebula and a separate color for the background (the inside of the nebula where the piece is primarily soft and flowing).

Iterator 1

Set the palette location to:

0.75

Set the blend speed to:

0.03

Iterator 2

Set the palette location to:

0.14

Set the blend speed to:

0.44

Iterator 3

Set the palette location to:

0.37

Set the blend speed to:

0.18

Iterator 4

Set the palette location to:

0.3

Set the blend speed to:

0.03

Iterator 5

Set the palette location to:

0.99

Set the blend speed to:

0.06

Iterator 6

Set the palette location to:

0.60

Set the blend speed to:

0.32

Iterator 7

Set the palette location to:

0.57

Set the blend speed to:

0.03

Adjusting Settings and Curves

There's one last step to bring this piece together: adjusting the response curves and some of the settings for the image. Open "Imaging Settings" if you don't already have it open, then set Brightness to 12.0, 1/Gamma to 1.6, and the Gamma Threshold to 0.0.

We're also going to want to set up the response curves as follows:

Screen Shot 2018-11-04 at 12.17.36 PM by ThoughtWeaver

Make sure you setup the background color to (0.03, -0.03, 0.08) and check the box that says "Apply before curves."

Then, go through each of the other channels, RGB, and adjust the curves to be as follows:

Screen Shot 2018-11-04 at 12.17.41 PM by ThoughtWeaver Screen Shot 2018-11-04 at 12.17.44 PM by ThoughtWeaver Screen Shot 2018-11-04 at 12.17.46 PM by ThoughtWeaver

And now we're done!

Screen Shot 2018-11-03 at 5.14.08 PM by ThoughtWeaver

Note: If you want a blurring effect, try adding some pre-transforms with Gaussian set to a really small value (around 0.02-0.05) in a couple of the iterators.

Know that none of these values are magic numbers; I highly recommend that you continue to tweak your fractal, experimenting with new variations, transforms, and xaos weights. Thank you for taking the time to read this tutorial and happy fractaling!

Comments


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:iconeknick14:
eKnick14 Featured By Owner Oct 14, 2018  Student General Artist
Hi there! :wave: I just wanted to thank you for joining our group, UnlimitedEverything, and that we hope you have an awesome time with us! We can't wait to see what you post next. Thank you again, and keep up the great work! :)
Reply
:iconbgai:
BGai Featured By Owner Aug 17, 2018
Hello Logan!! Welcome to :iconall-fractal-art: Thanks for joining!! If you haven't already, please be sure to read the group guidelines and rules on the front page before submitting :) (Smile) Keep you eyes out for the monthly polls and themes for features! :) (Smile)
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:iconthoughtweaver:
ThoughtWeaver Featured By Owner Aug 17, 2018  Hobbyist Digital Artist
Thank you! I'll be certain to do so. :D
Reply
:icon3days2go:
3Days2Go Featured By Owner Aug 13, 2018  Professional General Artist
:+favlove: Thank you for adding this to your faves collection!

They've Landed by 3Days2Go
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:iconthoughtweaver:
ThoughtWeaver Featured By Owner Aug 13, 2018  Hobbyist Digital Artist
Certainly! Congrats on the DD! :D
Reply
:iconzielinskimaciej:
ZielinskiMaciej Featured By Owner Jul 29, 2018  Hobbyist General Artist
Hi,
Many thanks for the :+fav: on the:
The 19th of May 2018 by ZielinskiMaciej
Much appreciated!!!:hug:
Reply
:iconhassanlechkar:
HassanLechkar Featured By Owner Jul 6, 2018  Hobbyist General Artist
Hi, just heard about your trip to DeviantArt HQ
Reply
:iconthoughtweaver:
ThoughtWeaver Featured By Owner Jul 7, 2018  Hobbyist Digital Artist
Yeah, it was awesome! :D
Reply
:iconbaspunk:
baspunk Featured By Owner Jun 11, 2018
merci :)
Reply
:iconrationalparadox:
RationalParadox Featured By Owner May 16, 2018  Hobbyist General Artist
Happy birthday!  :D
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