## Monthly Archives: January 2020

### Fractals in matlab/octave

Codes in matlab/octave for generating some popular fractals:

Mandelbrot

``` ```

```function mandelbrotmain() clear variables; clc;```

maxit=200;
x=[-2,1];
y=[-1 1];

xpix=601;
ypix=401;

x=linspace(x(1),x(2),xpix);
y=linspace(y(1),y(2),ypix);
[xG, yG]=meshgrid(x,y);

c=mb(maxit,xG,yG);

figure
imagesc(x,y,c);
colormap([1 1 1;0 0 0]);
axis on;
grind on;

endfunction

function count=mb(maxItr,xG,yG)
c=xG+1i*yG;
count=ones(size(c));
z=c;

for n=1:maxItr
z=z.*z+c;
inside=abs(z)<=2;
count=count+inside;
endfor
endfunction

Sierpinski triangle

``` ```

```clc; clear variables; close windows;```

clf

N=500;
x=zeros(1,N);y=x;r=x;
for a=2:N
c=randi([0 2]);
r(a)=c;
switch c
case 0
x(a)=0.5*x(a-1);
y(a)=0.5*y(a-1);
case 1
x(a)=0.5*x(a-1)+.25;
y(a)=0.5*y(a-1)+sqrt(3)/4;
case 2
x(a)=0.5*x(a-1)+.5;
y(a)=0.5*y(a-1);
end
end
plot(x,y,’o’)
title(‘Sierpinski’s triangle’)
legend(sprintf(‘N=%d Iterations’,N))

Fractal tree

``` ```

```function treemain tic clear all; depth = 7; figure 1; hold on;```

drawTree2(0, 0, 90, depth);
toc;
endfunction

function drawTree2(x1, y1, angle, depth)
deg_to_rad = pi / 180.0;
rot=30; #degrees :: rotation from second iteration
branchLength=100*depth;
if (depth != 0)
x2 = x1 + cos(angle * deg_to_rad) * branchLength;
y2 = y1 + sin(angle * deg_to_rad) * branchLength ;
line([x1, x2], [y1, y2],’LineWidth’,depth);
drawTree2(x2, y2, angle – rot, depth – 1);
drawTree2(x2, y2, angle + rot, depth – 1);

endif
endfunction

A note on fractal (from HH Hardey):
There are upper and lower limits to describe natural objects by fractals. A figure may look like a fern leaf, but continued generation of the “leaf on larger and larger scales produces only a larger and larger fern leaf. A fern “plant” will never be produced. Similarly, there is a smallest scale to which a fractal description applies. As the overall fern leaf pattern is repeated on smaller and smaller scales, eventually the scale of a single fern plant cell will be reached. A single cell does not look like the overall shape.

### Using Math Kernal Library (MKL) in visual studio with Fortran

First install MKL from intel website

To use intel MKL library inside visual studio do the followings:
1. Right click the project>Properties
2. In Property page>Fortran>Libraries set (a) Runtime library : Multithreaded and (b) Use Intel MKL: Sequential

Once this setting is done, you can compile the file in DEBUG mode. Repeat the same process (1-2) for RELEASE mode too once more.(Note exe of DEBUG mode is far slower than exe of RELEASE mode. The settings to set are listed below.

To do the same thing MANUALLY (which gives more insight to the code) do the following in each DEBUG and RELEASE mode.
1. Property page>Fortran>General>Additional Include Directories: C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.4.245\windows\mkl\include
2. Property page>Fortran>Preprocessor>Preprocess source file: Yes
3. Property page>Linker>General>Additional Library Directories:C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.4.245\windows\mkl\lib\ia32_win

The manual setting is described in the video as well:

For method to install Fortran in visual studio see this post.