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This Is Kelson's Blog=D
Please No Flaming/Spamming here as it may get you banned from my CBox =(
Leave a tag here if you want to =P
And lastly, Thanks for dropping by. =D
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name; Kelson
school; Yuying
Garena Name; Tone-
Email; shadowgrave92@hotmail.com
Birthday; 30th April 1992
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Sunday, June 20, 2010 @ 2:02 AM
MATHS MATHS AND MORE MATH
GG gonna fail
Maths for the generally stupid and retarded just taught me that:
The general formula to compute the fractal dimension is:
D = log(N)/log(1/r)
where r = scaling down ratio, and N = number of replacement parts.
For the Koch curve, the number of new units is 4, and the scaling down factor is 1/3. Thus
D = log(4)/log(3) = 1.261859
The length of the Koch curve L is given by the formula:
L = (4/3)n l
Self-similarity objects can be generated by mathematical formula such as:
z(n+1) = f [z(n)]
where z(n) is the nth iteration of the variable z, and f is a function of z. If we apply the iteration process even to very simple formulae using complex number, we can enter a fabulous world made of strange shapes and sometimes of astonishing beauty. For example:
z(n+1) = z2(n) + c
where z = x + iy (x is the real part, y is the imaginary part) is a complex variable and c is a complex constant.
Starting with an initial value z(0) equal to the coordinates of each point of the complex plane (imaginary axis in the vertical, real axis in the horizontal), the function diverges (the value of z' moves more and more away from the initial value) for many of such points. On the other hand, for some points, the result remains definitively within a limited interval : the function does not diverge, even for an infinite number of iterations. The points for which the function does not diverge give a set called connected Julia set (diagram a, Figure 13). In some cases a Julia set is fragmented (disconnected) as shown in diagram b. If, instead of giving c a fixed and arbitrary value, we give for any point of the complex plane an initial value c = z(0), we obtain a more complex mathematical object called the M (Mandelbrot) set (the black part at the center of diagram c). The points for which the values of z diverge do not belong to the filled-in Julia set: they are situated outside. But one can obtain extra information by giving them a brightness or a colour that is a function of the number of necessary iterations to observe the divergence. In other words this colour is a measure of the speed at which the function diverges for this point.
And for Non-linear Dimensions.
x: rotational speed of the convectional rolls (and the waterwheel),
y: temperature difference between p and q,
z: deviation of temperature from the mean,
: Prandtl number = (fluid viscosity/thermal conductivity),r ~ Rayleigh number (used in heat transfer and free convection calculations),
b ~ width/height.
(1/2) d{x2(t) + y2(t) + [z(t) - r -
]2} / dt = - {x2(t) + y2(t) + [z(t) - (r + )/2]2} + b [(r + )/2]2The left hand side of this equation describes the helical trajectory F2(t) = {x2(t) + y2(t) + [z(t) - r -
]2} / 2. The rate of change as indicated on the right hand side is negative for large value of (x,y,z). It means that the path spirals inward when it is far away from the origin. For small value of (x,y,z) the rate of change is positive (for b > 1), which means moving outward. Thus, points on the orbit outside the Lorenz attractor (in the shape of an "8") always return to the compact region and hence the name.
Bet no one i know can help me with that. =.=
Last time it was cubic equation and now this....
GG HO SEH LIAO.
NO NEED PASS LIAO.
CUBIC EQUATION TOOK ME WEEKS TO REMEMBER AND NOW CHAOS MATHS IS SCREWING ME =.=
GGWP
FailDieMe
EmoDieMe
At least one good thing came out of this week.
Watched A-Team
(Y) Movie
Too bad karate kid was sold out D:
Aww well stop here for now! :D
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Idiot maths... SCREW YOU
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