Ok, pitaću drugara ovih dana.

_Edit.
Samo da dopunim: relativno "neverovatno visoka", jer... ipak počinjemo od toga da smatramo i verujemo da to niko ne bi ni kupovao, jelte.  I da je bezvredno, u novčanom smislu. 
Što u prevodu znači, par stotina evra u vrh glave.  (al' malo li je na ovu zimoću  )

evo samo za snesku i njenu mamu

Ok, sad za munku znamo da se zove Snezana :duh: 

Evo o nekim fraktalima (koga ne mrzi):

Koch Snowflake



A fractal, also known as the Koch island, which was first described by Helge von Koch in 1904. It is built by starting with an equilateral triangle, removing the inner third of each side, building another equilateral triangle at the location where the side was removed, and then repeating the process indefinitely. The Koch snowflake can be simply encoded as a Lindenmayer system with initial string "F--F--F", string rewriting rule "F" -> "F+F--F+F", and angle 60 degrees. The zeroth through third iterations of the construction are shown above. The fractal can also be constructed using a base curve and motif, illustrated below.



Let N_n be the number of sides, L_n be the length of a single side, l_n be the length of the perimeter, and A_n the snowflake's area after the nth iteration. Further, denote the area of the initial n=0 triangle Delta, and the length of an initial n=0 side 1. Then
N_n   =   3·4^n   
(1)
L_n   =   (1/3)^n   
(2)
l_n   =   N_nL_n   
(3)
   =   3(4/3)^n   
(4)
A_n   =   A_(n-1)+1/4N_nL_n^2Delta   
(5)
   =   A_(n-1)+1/3(4/9)^(n-1)Delta.   
(6)

Solving the recurrence equation with A_0=Delta gives
A_n=1/5[8-3(4/9)^n]Delta,    
(7)

so as n->infty,
A_infty=8/5Delta.    
(

The capacity dimension is then
d_(cap)   =   -lim_(n->infty)(lnN_n)/(lnL_n)   
(9)
   =   log_34   
(10)
   =   (2ln2)/(ln3)   
(11)
   =   1.261859507...   
(12)



Some beautiful tilings, a few examples of which are illustrated above, can be made with iterations toward Koch snowflakes.


In addition, two sizes of Koch snowflakes in area ratio 1:3 tile the plane, as shown above.
http://mathworld.wolfram.com/images/eps-gif/KochFrillFlake3_1000.gif
Another beautiful modification of the Koch snowflake involves inscribing the constituent triangles with filled-in triangles, possibly rotated at some angle. Some sample results are illustrated above for 3 and 4 iterations.

Sierpiński Sieve




The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński gasket or Sierpiński triangle. The curve can be written as a Lindenmayer system with initial string "FXF--FF--FF", string rewriting rules "F" -> "FF", "X" -> "--FXF++FXF++FXF--", and angle 60 degrees.

Let N_n be the number of black triangles after iteration n, L_n the length of a side of a triangle, and A_n the fractional area which is black after the nth iteration. Then
N_n   =   3^n   
(1)
L_n   =   (1/2)^n=2^(-n)   
(2)
A_n   =   L_n^2N_n=(3/4)^n.   
(3)

The capacity dimension is therefore
d_(cap)   =   -lim_(n->infty)(lnN_n)/(lnL_n)   
(4)
   =   log_23   
(5)
   =   (ln3)/(ln2)   
(6)
   =   1.584962500...   
(7)

(Sloane's A020857; Wolfram 1984; Borwein and Bailey 2003, p. 46).

The Sierpiński sieve is produced by the beautiful recurrence equation
a_n=a_(n-1) xor 2a_(n-1),    
(

where xor denote bitwise XOR. It is also given by
a_n=product_(j; e(j,n)=1)2^(2^(e(j,n)))+1,    
(9)

where e(j,n) is the (j+1)st least significant bit defined by
n=sum_(j=0)^te(j,n)2^j    
(10)

and the product is taken over all j such that e(j,n)=1 (Allouche and Shallit 2003, p. 113).


The Sierpinski sieve is given by Pascal's triangle (mod 2), giving the sequence 1; 1, 1; 1, 0, 1; 1, 1, 1, 1; 1, 0, 0, 0, 1; ... (Sloane's A047999; left figure). In other words, coloring all odd numbers black and even numbers white in Pascal's triangle produces a Sierpiński sieve (Guy 1990; Wolfram 2002, p. 870; middle figure). The binomial coefficient (n; k) mod 2 can be computed using bitwise operations AND(NOT(n), k), giving the sequence 0; 0, 0; 0, 1, 0; 0, 0, 0, 0; 0, 1, 2, 3, 0; ... (Sloane's A102037; right figure), then coloring the triangle black if the result is 0 and white otherwise. This is a consequence of the Lucas correspondence theorem for binomial coefficients modulo a prime number.

Barnsley's Fern



The attractor of the iterated function system given by the set of "fern functions"
f_1(x,y)   =   [0.85 0.04; -0.04 0.85][x; y]+[0.00; 1.60]   
(1)
f_2(x,y)   =   [-0.15 0.28; 0.26 0.24][x; y]+[0.00; 0.44]   
(2)
f_3(x,y)   =   [0.20 -0.26; 0.23 0.22][x; y]+[0.00; 1.60]   
(3)
f_4(x,y)   =   [0.00 0.00; 0.00 0.16][x; y]   
(4)

(Barnsley 1993, p. 86; Wagon 1991). These affine transformations are contractions. The tip of the fern (which resembles the black spleenwort variety of fern) is the fixed point of f_1, and the tips of the lowest two branches are the images of the main tip under f_2 and f_3 (Wagon 1991).

Box Fractal


The box fractal is a fractal also called the anticross-stitch curve which can be constructed using string rewriting beginning with a cell [1] and iterating the rules



An outline of the box fractal can encoded as a Lindenmayer system with initial string "F-F-F-F", string rewriting rule "F" -> "F-F+F+F-F", and angle 90 degrees (J. Updike, pers. comm., Oct. 26, 2004).

super.. ja znam da pravim fraktale u GIMPu 

 

Mali update - Posto se sajt menja (prilagodjava novom konceptu) i u fazi reDizajna je sad cu da osvezim linkove ka novim - starim radovima (jer su ovi zastareli tj. nevide se slike) i dodam najAktivniji profil na DA i ...

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Sjajno

bas su interesantni pogotovo poslednji

Upravo tako!