This
tutorial will equip you with the skills to create a style of fractal
known as tiles. The concept of a tile (think subway tile or kitchen
backsplash) is ideal for a fractal application because of the
repeating pattern of self-similarity. In this tutorial we will
explore the power of post-transforms, learn how to apply a final
transform, and explore different formulas known as variations within
the Apophysis program.
Explanation
of Tiles
The
fractal tile style comes in a wide variety of shapes, from squares to
hexagons and beyond. All of them follow the same basic ideas to
create a pattern. Once you’ve conquered the structure for a tile, the
possibilities are literally endless, with a whole plethora of fun
formulas to be added and shapes to explore. Today we will focus our
attention on the basic square tile.
1. Basic
Structure of a Square Tile
Step 1
To
begin creating the structure for our square-tiled fractal, open the
Editor and click the button for a New/blank flame.
Step 2
The
next step is to set up the first transform. We do this because it will
serve as a template for the rest of the tile structure. Setting up
this one transform and copying it saves us a lot of time and work, and
is also good practice because it prevents us from making easy
mistakes by forgetting steps or mistyping values.
We
will leave the Variation set to linear=1 as the linear formula is the
backbone of this type of tile. Change the Weight of Transform 1 to
10. On the Colors tab, set the Color Speed setting to 1. The effect of
this will not be apparent right now, but will become evident as we
continue.
Step 3
Finally,
we need to move this initial transform into place. Move Transform 1
left one unit. Move this same transform up one unit.
Step 4
Now
that the first piece of our tile is in place, we can create the rest
of the tile structure. Each of these transforms will be a duplicate
of the first transform we setup.
Duplicate
Transform 1 by clicking the Duplicate Transform button at the top of
the editor. Move this transform to the right by two units.
Step 5
Duplicate
Transform 2 by clicking the Duplicate Transform button. Move
Transform 3 down by two units.
Step 6
Lastly,
Duplicate Transform 3. Move this transform to the left by two units.
This
completes the basic structure of a square tile.
2. Add the First Shape
The
number of options for putting shapes into fractal tiles is
staggering. For this tutorial, we’ll look at a few different
variations and how they can be used to create some amazing artwork.
Step 1
Create
a New Transform.
Step 2
At
this point, it is good to have the variation preview turned on in the
editor. This allows us to see what the particular variation is doing
on the fractal plane. It also allows you to visualize what each
transform’s effect is on the fractal and can provide invaluable
information as you design your own fractals.
Right-click
in the grid-portion of the editor window and choose the option Show
variation preview.
Step 3
For
this transform, we need to use the Variations tab of the editor.
Remove the 1 from Linear by changing it to a 0. You should now see
many small dots in the preview window. This shows you the structure
of the tile we set up. To get an even clearer picture, scroll down to
find the Blur variation and add 0.5 to Transform 5. You will see the
dots become clearer. Change the Blur value back to 0 to continue.
Step 4
To
begin adding some shape to our tile structure, find the variation
Bubble and change the 0 to 1.
Step 5
At
this point, the Bubble variation is too big to be useful in our tile.
We could reduce the amount of the variation to 0.25 or perhaps even
smaller. However, by doing so, we reduce the affect of the variation,
which is not what we’re aiming for as it will affect the shape.
Instead we are going to force the transform to become smaller and at
the same time retain the round shape of the Bubble variation when set
to 1. This is an incredibly powerful technique that will allow you to
retain the shape of a variation known as
post-transform. This is an over-simplified explanation, but use it to
your advantage: when you activate the post-transform, you keep the
original shape and can move it at will.
To
activate the post-transform mode, look for the button in the top menu
bar of the editor that has a Px and a triangle. Click this button to
enter the post-transform editing mode.
Step 6
With
the post-transform mode active, switch to the Triangle tab. We want
to shrink the size of Transform 5. Change the value in the Scale Box
(the one with a triangle on either side) to 200. Click the Scale Down
Triangle twice.
Step 7
We
can edit the shape of this transform more by deactivating the
post-transform mode and then scaling down the transform two more times
by 200.
Step 8
The
next step is to add more structure. Create a New Transform. Remove
the Linear variation by changing it to 0. Add Cylinder to this
transform by changing its value to 1. The cylinder variation will
give a long bar or tube shape.
Step 8
Once
again, at a value of 1, the cylinder transform is too large to fit
nicely into our tile. It needs to be scaled down just as the bubble
transform was. Enable post-transform mode, and scale down Transform 6
by the value of 200 three times. In the preview window, you’ll now see
the circles from the bubble transform appear connected by a long bar
which is our cylinder transform.
Step 9
Let’s
modify this transform some more. With post-transform mode still
active, move Transform 6 to the left 0.5 units and up 0.5 units.
Rotate this transform 45 degrees counter-clockwise. Notice that each
time we modify the position of this transform, the shape does not
change, only the position. This is the power behind the
post-transform mode. If we were to perform these same actions with
post-transform turned off, the entire shape of the fractal would
change drastically.
Step 10
We
can get more shape out of this transform by one more trick. Turn
post-transform mode off, and scale down this transform by 200 once.
This technique will put more texture into the transform and give us a
more 3D appearance.
Step 11
To
frame out the rest of our shapes, duplicate Transform 6. Enable
post-transform mode once again. This time, rotate Transform 7 90
degrees clockwise and move it one unit to the right.
3. Creating
a More Complex Structure
Step 1
We’ve
now completed a very basic tile structure and shape. Add a New
Transform and remove the linear variation from this transform by
changing Linear from 1 to 0. Change the values of Juliascope in the
Variations tab from 0 to 1. Enable the post-transform mode and scale
down by 200 and then again by 125. Move this transform up one unit.
Finally, switch to the Variables tab and change the juliascope_power
to 2 and juliascope_dist to 1. These modifications really fill in the
rest of the fractal and give it a solid and powerful appearance.
Step 2
Now
is a good time to adjust the weights of transforms. Originally we set
the weight of the first four transforms to 10. This allows the
structure of the tile to hold despite how many more additional
transforms we add, allowing us to continue to see what the tile looks
like while we design it.
Change
the weight of the transforms to the following:
- Transform
5: Bubble: 2 - Transforms
6 and 7: Cylinder: 3 - Transform
8: Juliascope: 3
Notice
how changing these weights affects the overall appearance of the
fractal. You may also notice a few annoying bright spots near the
middle of the fractal. (This will depend on your current gradient).
Let’s fix those now.
Step 3
Switch
to the Colors tab. For each of the transforms 5 through 8, change the
Opacity value from 1 to 0. Pay careful attention to the preview
window as you make each change and notice how the bright spot changes
to conform to the same color values as the rest of the fractal.
Step 4
This
is a good time for us to pick a color palette for the finished
fractal. Close the Editor and open the Gradient selection window.
Choose gradient 558_Explosion.
Step 5
Close
out of the gradient selection and open the Editor window. Open the
Colors tab. Remember when we set each of the linear transforms to a
color speed of 1? We did this so that all of the color changes we
make now will be consistent across the entire fractal.
Make
the following changes to each of the transforms:
- Transform
5: Transform Color: 0.150 and Color Speed: -1 - Transform
6 and 7: Transform Color: 0.708 and Color Speed: -1 - Transform
8: Transform Color: 0.608
To
give more prominence to the Juliascope transform (Transform 8),
change the Weight from 3 to 4.
4. Adding a Final
Transform
Step 1
To
give our fractal more punch, we can add a final transform. The final
transform will affect the entire fractal shape by influencing it with
any formula or combination of formulas we choose.
Enable
the final transform by clicking the Fx button with the little
triangle at the top of the editor menu bar. You will see a grey
triangle appear in the editor.
Step 2
This
final transform begins just like any other new transform we add, with
the linear variation set to 1. Remove this by switching to the
variations tab and changing the value of Linear to 0.
Step 3
Add
to the final transform 0.5 of the Foci variation and notice the
change of the overall shape. Additionally, add in 0.1 Spherical.
There is a slight, but visually appealing change to the shape of the
fractal. Combining variations like this, even positive and negative
amounts, can create some incredible images.
5. Cleanup
and Rendering
The
last few steps involve cleaning up the fractal and rendering.
Step 1
Close
the editor and use the zoom and move tools in the main window to find a nice location on
the fractal to render.
Step 2
Open
the Adjustment panel and change to the Rendering tab. Change the
Gamma setting to 3.5 for a slightly clearer render.
Step 3
The
final step is to render the fractal. Open the Render dialog by
clicking the purple gear in the main window. From here, set the
Density to 10,000. The Filter Radius setting of 0.455 will work
nicely for the detail in this fractal. An Oversample of 2 is ideal.
Click Start to begin the render.
Explore
the different final transforms first. Add several. Use negatives.
Be bold! You will be amazed at the variety of images you can get just
from changing these. Next, challenge yourself by removing the final
transform and move some of the other transforms to new locations.
Then, try changing the variations to create something new. If you
would really like a challenge, start from scratch and try to create a
hexagon or other type of tile.
Below are a few samples of what you can create with fractal tiles and Apophysis.
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