华工数学试验-功课3-迭代与分形(国外英文资料).docVIP

华工数学实验-作业3-迭代与分形(国外英文资料) The math experiment reports Institute of electronics and information Professional class: communication engineering class 4 Study number: 201130301443 Name: li tenghui Experiment name: iteration and fractal Experiment date: 2013.04.7 The third experiment Experimental content For an equilateral triangle, each edge is iterated by the Koch curve, resulting in a fractal graph called the Koch flake. The program draws its graph and calculates the area of the Koch flake, and its fractal dimension. experiment Methods a Modelled on the Koch curve code on each side of the triangle Koch curve, and the function of the input parameter is the side of the triangle R and the number of iterations k, output Koch snowflake and snow area S. The KochSnow area derivation follows: The number of iterations k area S Zero: S = 1: S is equal to R2 plus (R) 2 times 3 2: S = R2 + (R) 2 * 3 + (() 2R) 2 * 32 3: S = R2 + (R) 2 * 3 + (() 2R) 2 * 32 + (() 3R) 2 * 33 ` ` ` ` ` ` N: S = R2 + (R) 2 * 3 + (() 2R) 2 * 32 + (() 3R) 2 * 33 +... 2 * 3 n (nR) So if you add this up, when Na is infinity, S is going to be infinity Source code: Function kochsnow (R, k) % R is the length of the positive triangle, k is the number of iterations P01 = [0, 0]; P02 = [R / 2, SQRT (3) * R / 2]; P03 = [R, 0]; % 3 a starting point S = 0; The % S is the area, and set it to 0 For line = 0:2, the operation of the Koch curve is performed on three sides If the line = = 0; P = [p01 and p02]; Elseif line = = 1; P = [p02 p03); The else line = = 2; P = [p03 p01]; The end N = 1; The amount of the line segment is stored at the initial value of 1 A is equal to cosine of PI over 3, minus sine of PI over 3, sine of PI over 3, cosine of PI over 3. The % transformation matrix is used to compute the new nodes For the s = 1: k J = 0; % j for the number of rows For I = 1: n Q1 = p (I, :); The starting point of the current line segment Q2 = p (I + 1:); The end point of the current line segment D is equal to q2 minus