Lesson 5: Mapping – the Kaleidoscope transformation

You can apply various effects to a fractal, one of which is the Kaleidoscope transformation. By applying this effect, you change the fractal into a symmetrical figure. You see a simple example below:

[figure 5.1]

To achieve a Kaleidoscope effect, go to the Mapping tab of the layer properties window in the right upper corner of the screen (figure 5.2).

[figure 5.2]

The mapping tab

If you haven’t applied mapping yet, the window on the Mapping tab will be empty. If you click on the add icon  , a popup window with various options appears (figure 5.3).

[figure 5.3]

I will discuss each two mapping options in turn in separate lessons. First, let’s look at the Kaleidoscope transformation. This transformation makes it easy to achieve very nice effects. Sometimes, it makes the fractal look like a flower, other times more like a mandala. Time to start playing around with it yourself!

I made the following fractal:

[figure 5.4]

I started with a Julia fractal and selected Direct Orbit Traps as an outside formula.

After you have done this, go to the Mapping tab and click on the add icon . In the dropdown list that appears now (figure 5.3), click on “Kaleidoscope.” It may happen that you no longer see anything in your fractal window. The Kaleidoscope transformation may have been applied, but it did not start from the center of the screen. In this case, check “Use Screen Center” (figure 5.5).

[figure 5.5]

My fractal will now look like this:

[figure 5.6]

A black line runs exactly down the center of my fractal now. Let’s eliminate it before we continue to look at the Kaleidoscope options. To this end, we need to turn the fractal a bit. This is easy to do using the Location tab. It’s a tab we haven’t used yet, but I use it often in combination with Mapping.

In the Location tab you see a box called “Rotation Angle” (figure 5.7).

[figure 5.7]

You can enter the angle at which the fractal needs to be rotated. You can use the dropdown menu for this purpose [icon 53], but you can also enter values manually. To get rid of the black line, it’s often enough to insert 0.1. In other words, one-tenth of a degree, so you don’t see that the fractal has been rotated. If that value is too low, increase it bit by bit until you no longer see the black line.

[figure 5.8]

My fractal now looks like in figure 5.8 – a floral fractal that looks like a Delft blue plate.

Like we saw in figure 5.5, the Mapping tab contains a number of items that we can all change.

Symmetry order

In Symmetry order, you can specify the number of fractal segments that are copied and rotated. This is set to a standard value of 8, but you can also select a lower value. You see the effects of lower values in figure 5.9:

[figure 5.9]

Play around with it. The best value depends on the fractal and the effect you want to achieve. Figure 5.10 shows the fractal with a value of 16. This makes the fractal look more like a mandala.

[figure 5.10]

Symmetry mode

The default setting of Symmetry mode is “reflective.” This means that the kaleidoscopic segments merge seamlessly, which is not the case for the options left or right. These options mean that only the right or left part of a segment is mirrored.

The last option you can select is “slice only.” If you click on this option, you only see a single slice. This may seem a bit supperfluous (what use is a single segment?), but you can also produce unusual effects.

Rotation angle

You can specify how much to rotate the fractal in this box. This is a bit different from the Rotation angle we used before in the Location tab. We used that Rotation angle to rotate the whole fractal, including the Kaleidoscope effect. Rotation angle in the Mapping tab rotates only the fractal, changing the Kaleidoscope effect. Figure 5.11 shows what happens to my fractal if I set the Rotation angle to 90 degrees:

[figure 5.11]

A bit stark, but if you zoom into the center and adjust the width and height of the fractal in the Image tab of the Fractal Properties window to make it square, it looks completely different again:

[figure 5.12]

Center (Re) and Center (im)

You can also choose yourself which part of the fractal should be at the center of the kaleidoscopic image. To do this, you have to remove the check mark from Use Screen Center.

Now go to the box Center (Re) and click on the right mouse button. This brings up an eyedropper icon . Click the eyedropper button.

Your mouse cursor will change into an eyedropper as soon as you move it over the fractal. Click on the spot where you would like the center to be, and the kaleidoscopic image will appear. You can do this as often as you like until you’re satisfied with the result. Create a new fractal first, because checking Use Screen Center will no longer bring back the original kaleidoscopic image. After experimenting with the eyedropper for a while, I get the following fractal:

[figure 5.13]

Other Kaleidoscope effects

Besides using the Kaleidoscope transformation to make circular shapes, you can use other features of the Kaleidoscope transformation. Symmetry occurs in a kaleidoscope. You can see shapes appear that result from the kaleidoscope’s mirror effect. If you find such an interesting shape, you can enlarge it and use it as a new fractal.

Let me give you one example. You see repetitive pairs of opposing spirals in figure 5.6 above. By enlarging two of these spirals, I get the following fractal:

[figure 5.14]

[figure 5.15]

This no longer looks like a kaledioscopic image at all; it has a much more theatralic effect. A good basis to build on. Or may the detail in the middle at the top is more attractive (figure 5.15)?

Caution! You can enlarge a kaleidoscopic image section only if you have not checked Use Screen Center. Otherwise, the center of your fractal will always be used as the basis for a new kaleidoscopic image.

Layers

The Kaleidoscope effect (mapping) is applied layer by layer. Thus, you can apply the Kaleidoscope effect to different layers and then merge them. Merging is explained in lesson 4.

Another nice mapping effect is the Lake effect. You can learn how to apply it in lesson 6.