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Intro|Page 2|Page 3|Page 4|Page 5|Page 6|Page 7|
Page 8|Page 9|Page 10|Page 11|Page 12|Page 13|Page 14
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Here is where we really start to experiment and use our imagination ( at least that's all we can use unless you have a strong math background,unlike me! ) This is where we input new "formulae", where you can start to write your own unique formulas. Click your right mouse button over image and select " Unique Editor".
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Input the formula in the example, in the top dialog box, EXACTLY and hit OK. (Make sure you add the plus & minus signs in the right spots!) Notice there are also two input boxes labeled "M-set" & "N-Set". For now, leave it at the default "M-Set" but try changing this parameter on your own later, using any formula you wish to try. Here is the formula to copy and paste into the input box. Z*C+C/(1-Z*Z)*91+C*C*C  |
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Most of the fractal art that you see on this site I have made from my own formula "conncoctions"! For better or worse! ;) The formulae I use are strictly from my own improvisation, (creative experimentation), and that has been to a great extent, the fun of "discovering" or creating new images. Initially I tried to understand how these formulae 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. They used different letters etc. & as I mentioned before, I am NOT a mathematician! ;) These tips are what I have found to work so far. I'm sure there are more ways to create these 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. The operators you can use include the following: - ( minus/subtract ), + ( plus/add ), * ( multiply ), ^ ( exponent / to the power of ), / ( divide ) Complex trigonometric functions include: 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 formulae.
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.
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 in parenthesis brackets ( ).
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 "recipe"!
On with the tutorial!
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*Graphics designed by Doug Harrington and all content of this web site are subject to copyright restrictions and may not be used for commercial purposes or distributed without permission. If you are interested in commercial use of this art or have questions about any use not stipulated you can E-mail me at Support@Fractalarts.com or select E-mail link above.