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Dear fractal artists,
Many times I heard some words to this effect: I hate math; I have no idea what is the meaning of mathematical terms like exponential, delta, square-root, sinus, atan, etc. Will I ever be able to write a fractal formula?
Well, in spite of what some will like you to think, writing a fractal formula needs no previous math experience. It is like a game. Learn a few simple game rules, and you are in! In this formula writing tutorial you will learn in a few minutes how to write your first formula, and then how to develop your skill, and make the formula to fit the graphical pattern you wish to get - well wishful thinking, even for the best pro writers. But to some extent in time and experience you may learn the typical graphical manifestations of each formula type, and use it to get your goal.
So how to write and set User Formulas? No problem - it is as simple as ABC, or better said as "Z" and "C" :-)
MBF specific instructions
Click on the "User Equation" button in the main menu of MBF. A pop-up "User Equation Dialog" box appears.
In the pop-up box fill in the "Equation Name" (top left) text-box. Use any name you like.
In the "Initial Z = " text-box type: 0 (zero); you may try the number 1 as well.
The "Z = " text-box is the place to type the math Formula itself.
Note: All the pictures on this page were saved directly from the MBF program in the png format. This means that they could be loaded into the MBF program and continue to be processed by it.
Tiera-Zon specific instructions
Click on the "Draw" tab in the top main menu of Tier-Zon. A drop-down box appears.
In the drop-down box click on the "Unique Editor Dialog" line.
In the top text-box line type in the fractal formula as described in the general section.
Iterations specific instructions
Click on the "Option" tab in the top main menu of Iterations. A drop-down box appears.
In the drop-down box click on the "Unique Editor Dialog" line.
In the top text-box line type in the fractal formula as described in the genera; section.
General formula writing instructions:
As easy as Z and C
Any formula should contain two letters: "Z" and "C".
No other letters are permitted, and both letters must exist.
The letter "Z" must appear at least two times, with a * sign (Multiplication) between them: Z*Z
Before the C you put either a + (plus) or a - (minus) sign.
So now the formula looks like this: Z * Z + C
Congratulations! You have written your first fractal formula! Z = Z * Z + C is a perfect legitimate formula of the Mandelbrot type, and with this formula I made picture 1.
Picture 1:
Formula: Z = Z * Z + C
You may use the letter "Z" many times in the formula, thus making a "Z Chain" with * signs between them, as following: Z * Z * Z * Z + C
Here I used 4 "Z" letters with multiplication signs between them. Picture 2 was created with this formula. And I may use a chain of 5 "Z" letters, like this: Z * Z * Z * Z * Z + C.
Picture 3 was created with this formula:
Picture 2.
Formula: Z = Z * Z * Z * Z + C
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Picture 3.
Formula: Z = Z * Z * Z * Z * Z + C
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The chain of "*Z" may be prolonged. Pictures 4 and 5 were created with 6 and 7 "*Z" elements:
Picture 4.
Formula: Z = Z * Z * Z * Z * Z * Z + C
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Picture 5.
Formula: Z = Z * Z * Z * Z * Z * Z * Z + C
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From now on it is only a matter of your imagination and the most prosaic method of "trial and error". You may add "Z"s and "C"s and use any of the math signs between them. Without knowing the meaning of it, if it as any, I have added the following combination to the formula in picture 4, so it is now: Z = Z * Z * Z * Z * Z * Z + 6 * C * Z + C
to create picture 6.
Picture 6.
Formula: Z = Z * Z * Z * Z * Z * Z + 6 * C * Z + C
| Sign | Name | Function |
| + | Plus | Addition |
| - | Minus | Subtraction |
| * | Asterisk | Multiplication |
| / | Slash | Division |
Up to now we have used only two math signs: the plus sign (+) and the minus sign (-). Now it's time to add some more math signs to play with. The 4 most popular math functions are of course the addition, subtraction, multiplication and division. Their equivalent computer signs are seen in the table on the left.
For the initial phase of your formula writing you will find it more then enough to use these four elementary signs. In chapter two we will learn to use the rest.
Go to Chapter II
Dr. Joseph Trotsky, May 2001
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