FAQS
Q: What is the Random Equation Generator?
Simply put, the Random Equation generator will generate a mathematical equation that you can use for various fractal programs, and other java scripts I have designed. It is designed both for ease of use (just click "do it" and an equation will pop out automatically), and for complete customization (from the overall design of the equation generated, to each individual variable available)
Q: How the heck do I use your equation generator for Ultra Fractal?
1. Go HERE (or follow the link for templates in the equation generator).
2. Copy one of the generic formula templates that you wish to the clipboard by clicking the button "Copy to clipboard" (use the "fractal formula template" and "julia fractal formula template" for fractal formulas, the "transformation formula template" for transformation formulas, and the "index coloring formula template" and "direct coloring formula template" for coloring formulas).
3. Open a formula file in Ultra Fractal for editing (file->open, then select the file), or create a new one(file-> new, the select the type of file . Remember that .ufm is for fractal formulas, .uxf is for transformation formulas, and .ucl is for coloring formulas) Paste the template the file .
4. Generate a random equation using the random equation generator. Use the buttons on the top to choose the main variable for the type of formula you are making (fractal, transformation, coloring, etc.), set the number of passes, and adjust the percentages (see below for an explanation of how these work, or follow the link for explanations in the equation generator), and click the button "Do It!". Copy the equation to the clipboard using the button "Copy to clipboard".
5. Erase the text <INSERT <type> FORMULA HERE> and paste your equation from the clipboard in its place.
6. Rename the formula (especially if you've made a lot of random formulas) and save the file.
That should be it! Use your new formula where appropriate in UF (fractal, coloring, and transformation sections) and N-JOY! Mess with the parameters for maximum effect! If you don't come up with anything after messing with the parameters, just edit the formula, and replace that old equation with a freshly generated one, then reload the formula.
Q: How do I use your equation generator for your Dabbler Formula Generator Java Script?
All you need to do is customize your equation (or don't customize anything if you don't want to), then generate a random equation by clicking the "do it" button, copy it to the clipboard using the "Copy to Clipboard" button, and paste it into one of the equation boxes in the dabbler formula generator.
Q: What are all the buttons and numbers for?
Here's an explanation:
Radio Buttons on top:
Fractal Formula: The main Variable is "z"
Transformation Formula: The main Variable is "#pixel"
Coloring formula: The main Variable is "#index"
Julia Fractal Formula: The main Variable is "c"
Custom Formula: Type in the box underneath anything you want to be the main variable (I set it to "CUSTOM")
Your Main Variable : Clicking on the buttons mentioned above will put a main variable in this box. Alternately, you can type in whatever you want to use as the main variable here. Whatever is in this box will be the main variable of the equation
Number of Passes: The number of times the generator runs. Each time it runs, it may generate one of any of the below. Bigger numbers = larger (and more complex) equations
Chance of Main Variable (Per pass): the chance that the main variable will be generated on each pass
Chance of Parameter (Per Pass): the chance that a user-definable parameter (p1 - p6) will be generated
Chance of Function (Per Pass): the chance that a function of a set of variables (either hard-coded like sin() or a user-defined function like fn1() ) will be generated on each pass
Chance of Editable Function (instead of hard-coded): the chance that a user-defined function ( fn1() - fn4() ) will be generated instead of a hard-coded (like sin()) function
Chance of Numerical Value (Per Pass): the chance a numerical value will be generated on each pass. Includes a checkbox if you want an integer or a float (good to get numbers between 0 and 1)
Chance of a Changing Variable (Per Pass): the chance that a variable that continuously changes (like #x, #y, #pixel, etc.) will be generated on each pass
Chance of a Constant (Per Pass): the chance that a constant value (#e, #skew, #length) will be generated on each pass
Numerical Maximum: The maximum value a number will have
Integers Only: Checking this box will force any numbers being generated to be an integer value (i.e. 3, instead of 3.485294187)
Non-Zero: Checking this box will insure that you will not have 0 as a numerical value (the function zero() still exists, though)
Parentheses Complexity: the greater the number, the greater the chance that parentheses () will be created. I made sure to clean up all the excess parenthesis, so there aren't 10 open parentheses "(" and 1 close parenthesis ")"
Q: Can I use this for programs other than Ultra Fractal?
Probably...I imagine it can be used anywhere you would be looking for a random equation. Some of the items generated may not work correctly with other programs (like constants, changing variables, etc.) If you don't want them in, set its percentage to 0% and you won't (99% of the time) see it show up. Otherwise, you can always "hand polish" the equation to your liking by editing it before you click on the "copy to Clipboard" button.
Q: I used this program to make a fractal formula in Ultra Fractal, but all I get is a blue or black screen. Is your program broke?
No. Sometimes, when you first load up a fractal formula using the random equation generator, it'll come out solid blue or black. Here are a few things you can do to coax a fractal out of your new formula:
Use the eyedropper to change the values of all of the parameters (make them non-zero)
Flip through the functions (sin, cotan, sqr, round, etc)
Change the value of the bailout
Zoom out of the fractal
If you are using the Julia fractal template, try switching to Julia form, even if the screen is black or blue
If those methods don't work, then just plug another random equation into the formula.
Q: The Index coloring random equations won't work in an Ultra Fractal Index Coloring formula. What gives?
Seems that you can't read from #index in an equation, but you can write to it (#index=z OK, #index= z + #index NOT OK). I used a workaround in the coloring templates, where you instead use a random fractal equation (z = )to power the coloring formulae. Don't use the #index main variable until I fix it.
Q: How do I set up/use the generator for Fractal Explorer?
1. Use a regular fractal (the icon that looks like a miniature Mandelbrot fractal). The generator will only work for those types of fractals.
2. Go under the menu Fractal->edit (or hit F6), and the editing window will pop up.
3. In the top left corner, click on the "User Formula" Tab.
4. Click on the "Clear" button (has an icon that looks like a pencil eraser). This sets up the generic fractal template.
5. Click on the Button that looks like a square root symbol ( \/`````` ) with a symbol in it (the button is just to the right of the clear button). Another window will pop up, asking for an equation.
6. Use the generator to generate an equation (make sure you initialized it to Fractal Explorer first!), and copy it to the clipboard.
7. Paste the equation into the window that asked for an equation (by default, it has "z*z+c" in it).
8. VERY IMPORTANT- scroll back to the beginning of the equation you just pasted, and DELETE THE "z =" part, or it will generate an error later on.
9. Click on "convert - output to clipboard". If you get the error message "Bad Input:7", that means you forgot to delete the "z =" from the beginning of the equation.
10. Now that you have your equation converted, look for the line "// write your formula here" in the code template window (should be near the bottom of the code template window). Highlight and delete that line, and the line underneath it.
11. Paste your converted equation into the empty space you just made.
12. Finally, hit the "Compile Button", and let the program work its magic. Your new fractal should be rendered in the little preview window!
Q: How do I set up/use the generator for TieraZon/TieraZon2?
1. Go Under the TeiraZon/TieraZon2 menu Draw->Unique Editor Dialog
2. Use the generator to generate an equation (make sure you initialized it to TieraZon first!), and copy it to the clipboard.
3. Paste the equation into the window that asked for an equation (by default, it has "z*z+c" in it).
4. VERY IMPORTANT- scroll back to the beginning of the equation you just pasted, and DELETE THE "z =" part, or it will generate an error "Invalid Expression". If you already deleted the "z =", and are still getting the "invalid expression" error, try generating another equation.
5. Set your values for u, v, and w in the appropriate boxes, and click OK to let TieraZon/Tierazon2 work its magic. Your new fractal should be rendered immediately!
Q: Can I download it to my computer for offline use? How must does it cost?
Sure. Go ahead. My generator is freeware, for use by all. The java script in the page is embedded, so just save the html only...Geocities tends to add advertisements to the bottom, but those can be eliminated by editing the page with notepad and editing out the ads on the bottom (so your computer won't try to go online to contact geocities and get the latest ad).
Q: Are there any other legal ramifications for using your program?
I only ask that, if you are planning on using the equation generator algorithm in another program, that you give me credit for my work. You don't have to credit me for the custom formulas you make with his program, although it would please me to know that it is being used by people other than me! Drop me an email via the button below, or in the random equation generator :)
Q: Can you make an initialization setting for X program?
I don't see why not. Send me an email and tell me what program you'd like to have an initialization setting for, and I'll get to it. It _would_ help, though, if you send me a list of the following items (so I don't have to do it myself ;) ). Some programs may not use everything mentioned below, so don't worry if you only have 2-3 lists. Here are the items:
1. operators used: Basic Arithmetic operations used on any numbers (Most I've seen use +, -, *, /, and ^. Some also use modulus (%)
2. Hard-Coded Functions: like sin(), cotan(), ln(), exp(), sqr(), sqrt(), zero(), flip() conj(), etc.
3. User Functions: The ones where the user can define which function they use in the formula (like fn1(), fn2(), etc.)
4. Changing Variables: Variables that change per iteration, like #iter, x, cpixel, #random, y, etc.
5. Constants: unchanging variables, like pi, e, g, etc.
6. User-Definable Parameters: Variables that the user can change before iterating the equation, like p1, p2, p3, etc.
If you can't (or won't) do that, at least give me a link to the program you want me to make an initialization for, so that I don't have to search all over the internet to download the program!
Q: Is there any way I can help you with your program?
Well, if you wish, I ask that you spread the word about this generator with other people. Drop a line on a forum, tell a friend, whatever! It's freeware, so you don't have to give money, nor will I ask for it. If I _do_ think of something else in the meantime, I'll put it here. But for now, I just ask for you to inform people about my random equation generator, so that they, too, can benefit from my work.
Hope that helps...
-Jayce Cruel, Author