DIR Return Create A Forum - Home
---------------------------------------------------------
WrecklessPK
HTML https://wrecklesspk.createaforum.com
---------------------------------------------------------
*****************************************************
DIR Return to: Spam
*****************************************************
#Post#: 163--------------------------------------------------
Succesful Mandelbrot drawer is succesful.
By: Dr House Date: May 31, 2013, 1:05 am
---------------------------------------------------------
HTML http://eypic.net/images/dra.png
HTML http://eypic.net/images/draw.png
HTML http://eypic.net/images/dr.png
Written in Java :3
(Second one uses colors to indicate the amount of iterations it
did before its |a| became > 2 or |b| became > 2
For those interested in fractals and mathematics I'll make a
quick tutorial on 'understanding Mandelbrot sets'
First of all: This fractal is based on complex numbers, therefor
to understand this fractal you must understand how complex
numbers work.
Complex numbers are not too hard, they are in the form a + bi
where a and b are real numbers and i? = -1
Addition of a+bi and c + di = (a+c) + (b+d)i
Multiplication of (a+bi)*(c+di) = ac + adi + cbi + bdi?
= (ab - bd) + (ad + cb)i
Squaring of (a+bi)? is simply using the (a+b)? = a? + 2ab+ b?
formula
(a+bi)? = a? - b? + 2abi
The mandelbrot set is defined as the set of complex numbers
which do not diverge to infinity when using the recursive
formula : Z(n+1) = (Zn)? + C, where n indicates the index and
not a multiplication
Z0 is equal to 0 and C is a complex number.
If you were to set C = 0 + 0i, then:
Z0 = 0
Z1 = 0? + C= 0
Z2 = 0? + C = 0? + 0 = 0, etc
-> C = 0 + 0i belongs to the mandelbrot set
If you were to set C = 1 + i
Z0 = 0
Z1 = 0? + 1 + i = 1 + i
Z2 = (1+i)? + 1+ i = (0 + 2i) + 1 + i = 1 + 3i
Z3 = (1+3i)? + 1 + i = (-8 + 6i) + 1 + i = -7 + 7i , as you can
see this is diverging, so 1 + i does not belong to the
mandelbrot set
One last thing that is required to understand how this works is
to understand how complex planes work, which is also very easy
The x axis represents the a value of a complex number z ( a +
bi) and the y axis represents the b value of z.
EDIT:
Came up with the idea to make the recursive formula cube the
previous term instead of squaring and came up with a nice
result:
HTML http://eypic.net/images/draw1.png
(a+bi)^4 = a^4 - 6a?b? + b^4 + 4a?bi - 4ab?i
->
HTML http://eypic.net/images/draw4.png
#Post#: 171--------------------------------------------------
Re: Succesful Mandelbrot drawer is succesful.
By: v Date: May 31, 2013, 1:11 am
---------------------------------------------------------
Dha fuq lol :P 2 hard
#Post#: 175--------------------------------------------------
Re: Succesful Mandelbrot drawer is succesful.
By: Dr House Date: May 31, 2013, 1:11 am
---------------------------------------------------------
Easy.
#Post#: 177--------------------------------------------------
Re: Succesful Mandelbrot drawer is succesful.
By: Legendary Date: May 31, 2013, 1:12 am
---------------------------------------------------------
Not used for mai brain.
#Post#: 192--------------------------------------------------
Re: Succesful Mandelbrot drawer is succesful.
By: v Date: May 31, 2013, 1:22 am
---------------------------------------------------------
Jon my brain dont get it so please teach me? :P
#Post#: 196--------------------------------------------------
Re: Succesful Mandelbrot drawer is succesful.
By: Dr House Date: May 31, 2013, 1:23 am
---------------------------------------------------------
L2 Be Smart Like Me.
#Post#: 202--------------------------------------------------
Re: Succesful Mandelbrot drawer is succesful.
By: v Date: May 31, 2013, 1:27 am
---------------------------------------------------------
Hmm teach me then i'll be :P
#Post#: 227--------------------------------------------------
Re: Succesful Mandelbrot drawer is succesful.
By: Legendary Date: May 31, 2013, 2:25 am
---------------------------------------------------------
were not all having brains as computers ;)
*****************************************************