Fractal Tutorial - Writing Fractal Formulas
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A few tips on writing your own formulas.

Most of the fractal art that you see on this site I have made from my own formula "conncoctions", for better or worse! ;) The formulas I use are strictly from my own improvisation, (creative experimentation), and that has been, to a great extent, the fun of "discovering" and creating new images.

Initially I tried to understand how these formulas were written, and even downloaded a couple of formula files I stumbled across on the web, but unfortunately they were written for Fractint (another fractal program) and wouldn't work. Each fractal program used it's own proprietary method, different letters, numbers, format etc. & as I mentioned before, I am NOT a mathematician! ;)

So, the following tips are what I found to work for creating your own formulas within this particular program. I'm sure there are more ways to create these formuals than what I can share, but hopefully this will get you started & at least give you a rudimentary understanding of how to go about it within this program. I have written a complete tutorial series dealing with this subject alone, so check it out when you are ready to tackle it.

So, what format do we use to write the formulas within Tiera-zon? First variables are the operators. The operators you can use include the following:

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

You can use complex trigonometric functions, which include:

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

The three complex variables that can be used in a formula as constants are u, v, and w. The parser automatically looks for the value of Z to be the complex number to be iterated and the value of C is used to represent the current pixel coordinate. You can also use the parenthesis brackets ( ) to enclose parts of formulas.

The default formula when you open up the editor is " z*z+c ". This is the now famous "Mandelbrot" formula.

Using the formula that we just input for our fractal in the tutorial, we can look at some of the variables that can be used.

z*z+c/(1-z*z)*91+c*c*c

We can use any of the complex trigonometric functions by inputing the functions into the formula as in the following examples. Notice how the trig function is followed by a part of the formula enclosed in parenthesis brackets ( ).

z*z+c/atan(1-z*z)*91+c*c*c

z*z+c/atan(1-z*z)/log(91+c*c*c)

Experiment! If what you input doesn't work, you'll get an error message. Try again! Interchange the operators, numbers, trig functions, Z & C values etc. Try modifing one function at a time and observe the result. You will be amazed at how one number, operator etc. can radically change the image!

Substitute a minus for a plus, or a multiply for a divide, add an atan or two, mix in a few C's and Z's and you will be on your way to creating your own fractal "recipes"!

On with the tutorial!

Fractal Tutorial Page 10
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