Fractal Formula Tutorial Page 4 - How to write your own unique fractal formulas

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So far we've started off with some very basic formulas, and saw how we can make some basic shape changes. Before we move on and apply any additional changes, I will explain the remaining variables that can be changed within any formula that you create.

The operators you can use in any formula include the following four operators:

- ( minus/subtract ), + ( plus/add ), * ( multiply ), ^ ( exponent / to the power of ), / ( divide )

There are several complex trigonometric functions we can use as well. Don't panic, all you need to know that these are available to use within the formula editor! You do not need to know specifically how they function. If you do wish to know how trig functions affect the formulas, take a trig class! That information is beyond the scope of this tutorial, or my interest!

The following 8 trig functions are the ones allowed for use within our formula editor:

atan, tan, acos, cos, log, sin, sinh, asin

There are also three complex variables that can be used in a formula as constants, which are u, v, and w. I rarely use these constants, but they are worth experimenting with, so keep in mind that they are available to you. These function just like the C, Z and number parameters, and you can enter them into the formula just like you would those parameters.

You can also use numbers in combination with the parameters. As an example, you could use 1.375*z*z+c*c, or 1.5^z*z+c, etc.

You can also include a formula within parenthesis brackets, and then add numbers outside (or inside) the brackets using any of the four operators. Like this: 1.5^z*z/c+c, or 1.5^(z*z/c*c).

Note that these last two formulas contain the same basic parameters, but how they are combined will totally change the image. In the first example you are taking the first Z paramter to the power of 1.5. In the second, you are taking the entire formula to the power of 1.5 by enclosing the basic formula within the parenthesis brackets.

1) Let's continue to modify our previous formula by adding some trig functions, and observing the results. First, in order to use the trig functions, the other formula parameters must be enclosed within parenthesis brackets, and the trig function is entered in front of the parenthesis brackets. Let's use our previous formula using the sinh trig function. Enter the following into the formula editor: sinh(z*z*z*z*z*z*z+c). ( Also note that the trig functions must be in lower case, or you will get an error message )

2) Big change, huh? ;-) Okay, let's try the same formula with a different trig function, atan. Enter the following: atan(z*z*z*z*z*z*z+c). As you can see this produces a less symetrical change.

Fractal Formula Tutorial Page 5