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I decided to write this tutorial as most of the IFS tutorials are focused on Apo, and don't really explore all the possibilities Chaotica offers: a nice and flexible transform system, allowing effects that cannot be achieved in Apo without resorting to complex weight and "xaos" structures.

I will present here 5 examples to illustrate those possibilities.

Before reading this tutorial, you may take a look at the tutorial below, as it may help to understand some of the examples:

Pre and Post variationsA quick tutorial about how variations (transforms), pre_variations (pre_transforms) and post_variations (post_transforms) work. Specifically, what happens when there is a mix of variations, for example. Or several post ariaions together.Shortly, pre and post variations work same way as pre and post linked transforms. As a consequence, there are some things that are equivalent: pre_variation = a pre linked transform with the variation (normal one, not pre) post_variation = a post linked transform with the variation (normal one, not post) variation1 + post_variation2 on same transform = pre_variation1 + variation2 on same transform Below, we...

Also, notice that the focus of this tutorial is to explain a technique and not to teach you how to make some specific setup.

Example 1: Blur with double spherical
The first example is based on the technique described here:

Filling in with bubblesLets take a look at frameworks where you have a circular hole that needs to be filled to create a pattern. The basic idea Here, you have a variation or a combination of variations that has a round hole, which you need to fill with something to create a round pattern:We have basically two elements here - the framework itself and the filler. Lets take a look at some frameworks and fillers. Plastics and Blooms There are many tutorials on those structures (both frameworks and fillers): And yeah, blooms are also plastics (just look at the transfor 2 of the 2D tutorial - linear + spherical) ;) Lets take a quick look on how it works. Below, I...

Lets first make the basic framework. Start with a New World, and add 2 iterators.

To iterator 1, add a new transform, with spherical = 1. Then, add a second transform with eyefish = 0.2.

Then, add a transform to iterator 2, with hemisphere = 0.4. And, back to iterator 1, set its weight to something like 10.

Now, lets edit the affite of iterator 1. Scale it down, and then move and rotate:

You should have something like this:

This is the base for this example. Now, we will use the tricks

Lets add some pre transforms to iterator 2, in the order listed below:
spherical = 1
pre_blur = 0.1
spherical = 1

This is something you cannot really do in Apophysis, as you don't have many pre_ and post_ transforms avaliable and cannot use more than one instance of same transform at once, unlike in Chaotica.

What does this thing do? First spherial inverts the thing inside the hemisphere, then pre_blur blurs the middle of it, and then second spherical inverts it back. This way, we get exactly the same thing, not inverted (as we inverted it twice, thats back to original ), but with blurred edges and sharper center:

We can develop this further. On iterator 2, remove all the pre and transforms we added. And replace them with the following setup:
Pre_transform: spherical 1
Transform: linear = 0.95
Transform: starblur = 0.05 (set power to 3 and range to 1)
Post_transform: spherical = 1
Post_transform: hemisphere = 0.4
Here, we did the same, but instead of pre_blur we used a mix of linear and starblur. The spherical pre_transform, again, does the inversion. The mix of linear and starblur creates a bokeh effect. Note that, to mix up properly, those two have to be in the regular transform slot. So, we place them as regular transforms, and then apply the second spherical as post_transform to invert it all back. Then, as we still need to put this all in a hemisphere, we add back the hemisphere, as the last post_transform.

Below, I added a crackle transform and messed up with weights a little bit to highlight the bokeh effect:

Example 2: several instances of the same transform
As we already observed in the example above, you can use multiple instances of the same transform. Here, we use the technique described in the tutorial below:

A new(?) apo trick - includes paramsIf you've been hanging around aposhack at all the past few days, you've probably seen me excitedly linking to images like these::thumb214577717: :thumb214712055:Well, now I'm going to teach you how to get that intertwining.We are going to start from the sphereye-bubble template that comes with Apo 7x. If, for some reason, you don't have that/don't know how to get to it/are using a different version of apo, here are the params: F73B41F53B41F33B42F13A42EF3A42ED3A43EB3A43E93943 E73944E63944E43944E23844E03845DE3845DC3845DA3746 D83746D63746D43747D23647D03647CE3648CC3648CA3548 C83549C63549C53549C3344AC1344ABF34...

Basically, lets start with the parameters we created in the Example 1. Then:
Toggle Camera transform
Add a new transform to Camera, with julian = 1 (set power to 5)
Add another transform to Camera, with julian = 2 (set power to 3)

In the tutorial I linked, FarDareisMai uses julian and julian2 - but we can achieve the very same effect in Chaotica by just using julian twice (as none of the special parameters of julian2 was really used). Also, this solution is slightely faster, which makes a difference for animations and large renders.

If you did everything correctly, you should have something like this:

And, with a few more tweaking (basically, I moved and rotated the affine of iterator 1, and also the camera transform):

Example 3: Double Bubble Simplified
With smart usage of pre_ and post_ transforms, we can basically avoid most of the "xaos" / weight use that Apophysis usually requires.

Lets take a look at the Double Bubble Tut by piethein21 .
You may also check my speed fractaling video: [link]

But, this time, we will use pre_ and post_ transforms to avoid messing up with weights.

Start with a blank world. In the editor, add a new iterator, with following transforms:
Pre_transform: spherical = 1
Transform: hemisphere = 1
Post_transform: mobius = 1

Add a second iterator, and add same 3 transforms to it, so both iterators are identical.

Curl, used in the original tutorial, is a particular case of mobius, which we will now set up to replace curl:
On iterator 1: set mobius re_b to -1 and re_c to 1
On iterator 2: set mobius re_b to 1 and re_c to -1

The result should look like this:

Move around the pre_affines to obtain different patterns such as one below:

Example 4: Flux Simplified
This is just another case of mobius usage to replace curl. You may take a look at more half plane ideas in the tutorial below:

Filling Half PlanesThere are a few variations that map the whole plane to a half plane. For example, flux, deltaA and several others (either by themselves or in combination).Lets first take a look at a few works featuring those and then learn how to fill it up. HALF PLANE Those transformations take the whole plane and map it into half plane, leaving the other half empty. Flux and DeltaA are two examples of such transforms.To see how it works, lets start with a simple checkboard pattern:Now, we apply Flux as camera transform (fx):And DeltaA:The checkboard patterns covers all plane, but after we apply flux, we have half of the plane empty. So, back to puzz...

Start with a new blank world, and add two iterators. Add the following transforms:
To iterator 1, add a flux transform
To iterator 2, add a hemisphere transform

Now, to iterator 2, add a mobius post transform, and set mobius re_b to -1 and re_c to 1:

Now, you should have something like this:

After scaling, moving and rotating the pre affines, you could end up with something like:

Example 5: Foci Simplified
And, of course, this wouldn't be me if i didn't find a way to put some foci into it.

Lets start with the parameters from the previous example. Toggle the camera transform, and add a hemisphere tranform to it. Then, add a ngon post transform (with ngon = 0.5), and set ngon power to 0:

Now, let's keep adding post transforms. First, add a tile_log post transform. Then, on top, add a mobius post transform. Set re_a to 0.785398 (as in pi/4), and im_a to 2.08.

Finally, add a foci post_transform (so you will have a whole 4 post transforms on your camera transform):

The result will look like this:

If you want to be really evil, you can, instead of putting this into cam transform, incorporate foci into the fractal itself.

To do this, add the following pre_transforms to iterator 2:
hemisphere = 1
ngon = 0.5 with power = 0
tile_log = 1
mobius = 1 with re_a = 0.785398 and im_a = 2.08
foci = 1
The result should look like this:

=) (Smile) — Description
/* Journal Top */ body div#devskin11548908 .gr-box { background:#617360; } body div#devskin11548908 .gr-top h2, body div#devskin11548908 .gr-top h2 a { text-transform:uppercase; letter-spacing:2px; padding:5px 20px; font-size:29px; } body div#devskin11548908 .timestamp, body div#devskin11548908 .commentslink { text-align:center; padding:5px; text-transform:uppercase; letter-spacing:2px; } body div#devskin11548908 .left { width:17%; } body div#devskin11548908 .right { width:83%; } body div#devskin11548908 .right { float:right; } body div#devskin11548908 .left { float:left; } /* Box and Square Headings */ body div#devskin11548908 h1, body div#devskin11548908 h2 { text-transform:uppercase; font-weight:normal; font-size:14px; font-weight:bold; font-family:'open sans'; } body div#devskin11548908 h1 { letter-spacing:2px; color:#fff; padding:5px; background:#617360; } body div#devskin11548908 .text h2 { padding-left:10px; letter-spacing:1px; margin:5px 0 -5px 0; border-left:20px solid #617360; } body div#devskin11548908 h1:hover, body div#devskin11548908 h2:hover { font-weight:bold; } body div#devskin11548908 .p1 { background:#617360; } body div#devskin11548908 .b1 { background:#617360; } body div#devskin11548908 .g1 { background:#617360; } body div#devskin11548908 .p2 { border-left:20px solid #617360!important; } body div#devskin11548908 .b2 { border-left:20px solid #617360!important; } body div#devskin11548908 .g2 { border-left:20px solid #617360!important; } /* Mini Gallery Code */ body div#devskin11548908 .mini .shadow-holder { display:inline-block; width:150px; height:150px; overflow:hidden; } body div#devskin11548908 .mini .shadow-holder img { padding:0px; max-width:none; margin:0 0 0 0; } body div#devskin11548908 .mini .lit { width:150px; height:150px; } body div#devskin11548908 .mini .shadow-holder:hover img, body div#devskin11548908 .mini .shadow-holder:hover .lit { position:absolute!important; z-index:2; margin:7px 0 0 -63px; padding:5px; } body div#devskin11548908 .b .shadow-holder:hover img, body div#devskin11548908 .b .shadow-holder:hover .lit, body div#devskin11548908 .embedded-deviation img:hover, body div#devskin11548908 .embedded-freeform-deviation:hover { background:#617360; } body div#devskin11548908 .g .shadow-holder:hover img, body div#devskin11548908 .g .shadow-holder:hover .lit, body div#devskin11548908 .embedded-deviation img:hover, body div#devskin11548908 .embedded-freeform-deviation:hover { background:#617360; } body div#devskin11548908 .y .shadow-holder:hover img, body div#devskin11548908 .y .shadow-holder:hover .lit, body div#devskin11548908 .embedded-deviation img:hover, body div#devskin11548908 .embedded-freeform-deviation:hover { background:#617360; } body div#devskin11548908 .shadow-holder:hover img, body div#devskin11548908 .shadow-holder:hover .lit, body div#devskin11548908 .embedded-deviation img:hover, body div#devskin11548908 .embedded-freeform-deviation:hover { background:#617360; } body div#devskin11548908 .mini.b .shadow-holder:hover { background:#617360; } body div#devskin11548908 .mini.g .shadow-holder:hover { background:#617360; } body div#devskin11548908 .mini.y .shadow-holder:hover { background:#617360; } body div#devskin11548908 .mini .shadow-holder:hover { background:#617360; }

I decided to write this tutorial as most of the IFS tutorials are focused on Apo, and don't really explore all the possibilities Chaotica offers: a nice and flexible transform system, allowing effects that cannot be achieved in Apo without resorting to complex weight and "xaos" structures.

I will present here 5 examples to illustrate those possibilities.

Before reading this tutorial, you may take a look at the tutorial below, as it may help to understand some of the examples:

Pre and Post variationsA quick tutorial about how variations (transforms), pre_variations (pre_transforms) and post_variations (post_transforms) work. Specifically, what happens when there is a mix of variations, for example. Or several post ariaions together.Shortly, pre and post variations work same way as pre and post linked transforms. As a consequence, there are some things that are equivalent: pre_variation = a pre linked transform with the variation (normal one, not pre) post_variation = a post linked transform with the variation (normal one, not post) variation1 + post_variation2 on same transform = pre_variation1 + variation2 on same transform Below, we...

Also, notice that the focus of this tutorial is to explain a technique and not to teach you how to make some specific setup.

Example 1: Blur with double spherical
The first example is based on the technique described here:

Filling in with bubblesLets take a look at frameworks where you have a circular hole that needs to be filled to create a pattern. The basic idea Here, you have a variation or a combination of variations that has a round hole, which you need to fill with something to create a round pattern:We have basically two elements here - the framework itself and the filler. Lets take a look at some frameworks and fillers. Plastics and Blooms There are many tutorials on those structures (both frameworks and fillers): And yeah, blooms are also plastics (just look at the transfor 2 of the 2D tutorial - linear + spherical) ;) Lets take a quick look on how it works. Below, I...

Lets first make the basic framework. Start with a New World, and add 2 iterators.

To iterator 1, add a new transform, with spherical = 1. Then, add a second transform with eyefish = 0.2.

Then, add a transform to iterator 2, with hemisphere = 0.4. And, back to iterator 1, set its weight to something like 10.

Now, lets edit the affite of iterator 1. Scale it down, and then move and rotate:

You should have something like this:

This is the base for this example. Now, we will use the tricks

Lets add some pre transforms to iterator 2, in the order listed below:
spherical = 1
pre_blur = 0.1
spherical = 1

This is something you cannot really do in Apophysis, as you don't have many pre_ and post_ transforms avaliable and cannot use more than one instance of same transform at once, unlike in Chaotica.

What does this thing do? First spherial inverts the thing inside the hemisphere, then pre_blur blurs the middle of it, and then second spherical inverts it back. This way, we get exactly the same thing, not inverted (as we inverted it twice, thats back to original ), but with blurred edges and sharper center:

We can develop this further. On iterator 2, remove all the pre and transforms we added. And replace them with the following setup:
Pre_transform: spherical 1
Transform: linear = 0.95
Transform: starblur = 0.05 (set power to 3 and range to 1)
Post_transform: spherical = 1
Post_transform: hemisphere = 0.4
Here, we did the same, but instead of pre_blur we used a mix of linear and starblur. The spherical pre_transform, again, does the inversion. The mix of linear and starblur creates a bokeh effect. Note that, to mix up properly, those two have to be in the regular transform slot. So, we place them as regular transforms, and then apply the second spherical as post_transform to invert it all back. Then, as we still need to put this all in a hemisphere, we add back the hemisphere, as the last post_transform.

Below, I added a crackle transform and messed up with weights a little bit to highlight the bokeh effect:

Example 2: several instances of the same transform
As we already observed in the example above, you can use multiple instances of the same transform. Here, we use the technique described in the tutorial below:

A new(?) apo trick - includes paramsIf you've been hanging around aposhack at all the past few days, you've probably seen me excitedly linking to images like these::thumb214577717: :thumb214712055:Well, now I'm going to teach you how to get that intertwining.We are going to start from the sphereye-bubble template that comes with Apo 7x. If, for some reason, you don't have that/don't know how to get to it/are using a different version of apo, here are the params: F73B41F53B41F33B42F13A42EF3A42ED3A43EB3A43E93943 E73944E63944E43944E23844E03845DE3845DC3845DA3746 D83746D63746D43747D23647D03647CE3648CC3648CA3548 C83549C63549C53549C3344AC1344ABF34...

Basically, lets start with the parameters we created in the Example 1. Then:
Toggle Camera transform
Add a new transform to Camera, with julian = 1 (set power to 5)
Add another transform to Camera, with julian = 2 (set power to 3)

In the tutorial I linked, FarDareisMai uses julian and julian2 - but we can achieve the very same effect in Chaotica by just using julian twice (as none of the special parameters of julian2 was really used). Also, this solution is slightely faster, which makes a difference for animations and large renders.

If you did everything correctly, you should have something like this:

And, with a few more tweaking (basically, I moved and rotated the affine of iterator 1, and also the camera transform):

Example 3: Double Bubble Simplified
With smart usage of pre_ and post_ transforms, we can basically avoid most of the "xaos" / weight use that Apophysis usually requires.

Lets take a look at the Double Bubble Tut by piethein21 .
You may also check my speed fractaling video: [link]

But, this time, we will use pre_ and post_ transforms to avoid messing up with weights.

Start with a blank world. In the editor, add a new iterator, with following transforms:
Pre_transform: spherical = 1
Transform: hemisphere = 1
Post_transform: mobius = 1

Add a second iterator, and add same 3 transforms to it, so both iterators are identical.

Curl, used in the original tutorial, is a particular case of mobius, which we will now set up to replace curl:
On iterator 1: set mobius re_b to -1 and re_c to 1
On iterator 2: set mobius re_b to 1 and re_c to -1

The result should look like this:

Move around the pre_affines to obtain different patterns such as one below:

Example 4: Flux Simplified
This is just another case of mobius usage to replace curl. You may take a look at more half plane ideas in the tutorial below:

Filling Half PlanesThere are a few variations that map the whole plane to a half plane. For example, flux, deltaA and several others (either by themselves or in combination).Lets first take a look at a few works featuring those and then learn how to fill it up. HALF PLANE Those transformations take the whole plane and map it into half plane, leaving the other half empty. Flux and DeltaA are two examples of such transforms.To see how it works, lets start with a simple checkboard pattern:Now, we apply Flux as camera transform (fx):And DeltaA:The checkboard patterns covers all plane, but after we apply flux, we have half of the plane empty. So, back to puzz...

Start with a new blank world, and add two iterators. Add the following transforms:
To iterator 1, add a flux transform
To iterator 2, add a hemisphere transform

Now, to iterator 2, add a mobius post transform, and set mobius re_b to -1 and re_c to 1:

Now, you should have something like this:

After scaling, moving and rotating the pre affines, you could end up with something like:

Example 5: Foci Simplified
And, of course, this wouldn't be me if i didn't find a way to put some foci into it.

Lets start with the parameters from the previous example. Toggle the camera transform, and add a hemisphere tranform to it. Then, add a ngon post transform (with ngon = 0.5), and set ngon power to 0:

Now, let's keep adding post transforms. First, add a tile_log post transform. Then, on top, add a mobius post transform. Set re_a to 0.785398 (as in pi/4), and im_a to 2.08.

Finally, add a foci post_transform (so you will have a whole 4 post transforms on your camera transform):

The result will look like this:

If you want to be really evil, you can, instead of putting this into cam transform, incorporate foci into the fractal itself.

To do this, add the following pre_transforms to iterator 2:
hemisphere = 1
ngon = 0.5 with power = 0
tile_log = 1
mobius = 1 with re_a = 0.785398 and im_a = 2.08
foci = 1
The result should look like this: