**Lesson 2: Choosing a formula**

Fractals are based on formulas. You can see and change the formula in the Layer Properties window (see figure 2.1) by clicking on the write icon .

[figure 2.1]

A pop-up window that shows a large number of formulas appears (to close the edit window, click the x in the top right corner).

Fortunately, UF comes with a large number of formulas. In this section, you will learn how to use the formulas included.

**Why should you use a formula?**

In the first lesson, you learned how to change a fractal by zooming in on parts of the fractal. No matter how far you zoom into the fractal however, it will never lose its shape; you will see the the same details over and over again.

A formula contains many values that are taken into account in calculations. These values ultimately determine the appearance of your fractal. You can easily change the values in many of the formulas supplied with UF. And because the outcome of that new formula depends on the fractal you’ve made, it’s always exciting to see the result.

Maybe the next steps will make this statement a little clearer:

**Opening a formula**

- Click the Outside tab in the Layer Properties window (figure 2.2).

[figure 2.2]

- Next, click the Browse icon.
- Select a formula from the Standard.ucl folder. Figure 2.3 shows you that I have selected Direct Orbit Traps.

[figure 2.3]

##### 2. **Changing the parameters**

Figure 2.4 shows you what the fractal looks like when I open the formula Direct Orbit Traps:

[figure 2.4]

This is a dark and not very interesting fractal. By changing parameters (values in the formula), we can look for a more attractive fractal.

Fortunately, most of the makers of the formulas have made things a little easier for us by giving the parameters in the Outside tab of the Layer Properties window names. In some cases, you can enter a value yourself, in others, you can choose a value from a list.

Let’s get down to business now. We can change the Trap Shape values. I have selected the value hypercross. Figure 2.5 shows my resulting fractal.

[figure 2.5]

We can change another parameter, too: Trap Coloring.

I set the value to at angle to trap, which produces the fractal you see in figure 2.6:

[figure 2.6]

In this way, you can change various parameters until you have a fractal you’re satisfied with. In my example, I changed Trap Shape first, then Trap Coloring. I could now test what happens to my fractal if I change Trap Shape (while leaving Trap Coloring unchanged at angle to trap).

Thus, you have endless possibilities. Don’t be afraid to play around with various parameters. If you change something but decide you like the previous fractal better, you can undo the change.

You can’t remember what parameters you had last? Press Control (Ctrl) on your keyboard and then click on Z. This will undo your last action.

Fine, now we have a fractal we’re happy with. Unfortunately, the colors are very dark. Time to move on to the next step: **Colors**.