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Math Pattern Generator

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Author: Xray

Group: Default

Filesize: 61.55 kB

Date added: 2015-12-08

Rating: 6.1

Downloads: 548

Views: 340

Comments: 21

Ratings: 3

Times favored: 0

Made with: Algodoo v2.1.0

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I was trying very hard to generate a Mandelbrot Fractal by programming the complex math algorithm. Well, after giving up on that, I started playing around with a lot of different math functions in order to try to get them to plot some interesting patterns of dots, and this is what I came up with. Follow the instructions in the scene.

BTW - If any of you math and programming wizards (you know who you are) want to work on a challenging but rewarding project, make a scene that generates a true Mandelbrot Fractal. My math and programming skills are not quite strong enough for such a project, and so I'm hoping that someone else can successfully do what I had failed at. :blush:
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Simply downloading crashes my iPad... I'll try this later when I get to my desktop PC.
Ohhhh, mandelbrot, I recoded that algorythm in java, so I could help you with that, if we use about 144 circles to represent the dots.
Awesomely cool.
I once tried to make the mandelbrot thing in Algodoo, after working for several hours, it worked with a slight error.
Anbang11 - Why didn't you post the scene? If you still have it, you can post it because I would like to take a look at it to see how you made it!
Mandelbrot is actually German, it means ???bread
For more information go to www.htwins.net/mandy
When I squared the mandelbrot equation (z^2+(x+yi)
I got (z^4)+(2z)+(2x)-(zy)+(x^2)-(xy)+(y^2)-(y)-1
I simplified until there were no "i"s left.
desmos is not capable of graphing it
NEXT TIME ON: THE MANDELBROT MYSTERY-
LastChance has the equation, but... Desmos is not capable of grahing it. So, he takes matters into his own hands. The end of this season might be on it way! (hopefully)
Well, I made it in quite a short time, but that's because I have done this before already ^^.

Also, about the formula with the complex numbers:

C^2 = (Cx+Cy*i)^2 = Cx*Cx + 2*Cx*Cy*i+Cy*i *Cy*i ) Cx^2 + 2CxCyi + Cy^2 * (- 1)

Short version: C^2 = (x^2-y^2,2xyi)
XRAY PLZ STOP SENDING ME SPAMS ABOUT UR NEW SCENES!!!
austin9700 - I have no idea what you are talking about! I don't send you anything at all. Maybe it's because you are subscribed to me, the Algobox system automatically sends you information about new scenes that I post. If that's it, then just unsubscribe from me and you should no longer receive those "spams".:rolleyes:
FRA32-
Is that mandebrot equation? I thought it was C^2=(x+yi)^2+c
I squared it, and that is what I got.
wait
I think I did it wrong
(everybody but me facepalm)
:D
@Xray
I don't think you spam:D
@LastChance

You are PARTLY right, since any number consisting of (x+yi) is called a complex number. And since any number can be replaced with 1 sole variable, and since said variable is dependand on the last result, one says Xn+1 = Xn^2+C, which means the new complex number X is made of the last complex number X squared plus the complex number C, which consists of (x,yi) whereas x and y are the coordinates of the point that the set calculates.

Squaring any complex number is basically like working with a binomial formula:

(a+b)^2 = a^2+2*a*b+b^2

Since complex numbers also own the factor i, the formula is slightly modified, integrating i to all places where b occurs:

(x+yi)^2 = x^2 + 2xyi + y^2*i^2

and since i^2 = -1, and y^2 * -1 = -y^2, the formula finally turns into x^2 + 2xyi - y^2, and now you can easily reorder the parts to (x^2 - y^2 + 2xyi) and you've got the new complex number.
Last edited at 2015/12/19 08:57:50 by FRA32
When are you supposed to press Alt? I dont get it.
-Xray
My goal is to get desmos to graph the mandelbort equation. And not a whole bunch of points that look like it. The actual equation.
The way to do this is to not use "imaginary" and by getting rid of i, I must square it as many times as necessary to make -1.
While this answer is a little late, you can completely ignore the i part in the formula since you square the complex numbers, turning it into -1. So the formula is Zn+1(x,y) = (Zx^2-Zy^2,Zx*Zy)+(Cx,Cy). Your maths program does not care that there should be an i in the equation if you leave it out. Ss long as you tell it that the y coordinate turns negative when squared, even if common maths may return other things, it will return correct results. That's why algodoo can do this thing despite our lack of the complex number system.