Fractal Formula Tutorial Page 5 - How to write your own unique fractal formulas

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Hopefully the steps we have covered so far are beginning to illustrate that there are many creative opportunities within this program when using your own formulas. This is why I do not use the built in formulas, there's really no need to, and experimenting is far more fun than simply clicking a button that everyone else does! ;-)

1) Before moving on let's add a filter to the last image. From the Filter3 menu select Iterations FDimension.

2) While this is off topic a bit, it's a good opportunity to give you another tip. Notice how the image is surrounded by a circle that ends, and the blank area beyond? You can extend the range of the fractal by changing one parameter. Right click over the image and select Fractal Parameters.

3) By changing this one variable, the bailout, it will extend the iteration out from the original range. Keep in mind that this may, or may not, result in a change you want. Try smaller numbers, then larger to see how this affects the fractal change. For now, set it like the image below.

4) Now the bailout has been extended, and the blank spaces are gone, filled in by a great deal of detail. If there is too much detail, you can reduce it by setting the M-Set max setting to a lower number. This variable is also under the Fractal Parameters. For now let's leave it where it's at.

5) Ok, time to get back on track! This time we are going to continue to add on to our formula by adding additional parameters, and also combining another trig function. Open the Formula Editor and enter the following formula: asin(z*z*z*z*z*z*z+c)/-log(c*c*c). Note how this time we have added the negative operator, or minus sign, in front of the new trig function, "log".

This is another aspect of changing the trig functions. We can not only combine trig functions, but add negative operators with them. As you can see in the image below, this has dramatically changed our fractal again.

6) This time we will add a third trig function. First enclose the entire formula within parenthesis brackets, and then add the third trig function, -cos, in front of the formula. Here is the formula: -cos(asin(z*z*z*z*z*z*z+c)/-log(c*c*c)) If you get an error, be sure that the parenthesis brackets are in the correct places.

7) Here is the result of the last equation. As you can see there are unlimited possibilities for combining all of these various mathematical functions.

Fractal Formula Tutorial Page 6