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Chaos, Fractals, and Art

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ylim([0 dim]); 
 xlabel('r, box size'); ylabel('- d ln n / d ln r, local dimension'); 
 title([num2str(dim) 'D box-count']); 
elseif nargout==0 || any(strncmpi(varargin,'plot',1)) 
 loglog(r,n,'s-'); 
 xlabel('r, box size'); ylabel('n(r), number of boxes'); 
 title([num2str(dim) 'D box-count']); 
end 
if nargout==0 
 clear r n 
end 
 
 
 
 
 
 
 
 
 
 
 
Appendix B 
 
 
 
 
 
 
 
 
 
 
 
Appendix C 
Fern.m 
 
%Code credit to 
%http://www.mathworks.com/matlabcentral/fileexchange/16618-barnsleys-fern 
%parameters from Fractals Everywhere by Michael Barnsley 
%comments by Ali Lavine 
%Notation for IFS of affine map: 
% wj(x) = wj[x;y] = [aj bj; cj dj]*[x;y] + [ej; fj] = Aj*x + tj 
% where each j is a subscript, j = 1,2,3,4, and the total probability of 
% the wj's equals 1. 
n=70000; % number of iterations 
%IFS code for a Fern 
%a = [a1 a2 a3 a4] 
a=[0 0.85 0.2 -0.15]; 
b=[0 0.04 -0.26 0.28]; 
c=[0 -0.04 0.23 0.26]; 
d=[0.16 0.85 0.22 0.24]; 
e=[0 0 0 0]; 
f=[0 1.6 1.6 0.44]; 
%initialize variables 
x(1)=0; 
y(1)=0; 
j=0; 
%loop for each iteration 
for i=1:n 
prob=rand; 
%prob < p1 
if prob<0.01 
j=1; 
% p1 < prob < p1 + p2 
elseif prob>0.01 && prob<0.86 
j=2; 
% p1 + p2 < prob < p1 + p2 + p3 
elseif prob>0.86 && prob<0.93 
j=3; 
else 
j=4; 
end 
x(i+1)=a(j)*x(i)+b(j)*y(i)+e(j); 
y(i+1)=c(j)*x(i)+d(j)*y(i)+f(j); 
end 
plot(x,y,'g.','MarkerSize',1) 
 
 
 
 
 
 
 
 
 
 
 
i Briggs, John. Fractals the patterns of chaos: a new aesthetic of art, science, and nature. New York: Simon & 
Schuster, 1992. 28. 
ii “The Mirror”, chapter 0 of Turbulent Mirror, an illustrated guide to chaos theory and the science of wholeness, 
by John Briggs and F. David Peat, 1989 Editor’s note: the mirrorlike structure of this volume makes chapter 0 
the fifth chapter in the book., pp 83-113. 112. 
*Citation from compilation by Professor Wallace entitled Mathematics 7, Attractive Disorder: Chaos in 
Literature, Mathematics and Beyond. Winter, ’98. 
iii "The Great Wave at Kanagawa (from a Series of Thirty-six Views of Mount Fuji) | Katsushika Hokusai | All | 
Asian Art | Collection Database | Works of Art | The Metropolitan Museum of Art, New York." The 
Metropolitan Museum of Art, New York: metmuseum.org. Web. 04 Dec. 2009. 
<http://www.metmuseum.org/works_of_art/collection_database/asian_art/the_great_wave_at_kanagawa_from_
a_series_of_thirty_six_katsushika_hokusai/objectview.aspx?collID=6&OID=60013238>. 
iv Txopitea, Ainize. "Www. yochaos.com." AINIZE TXOPITEA. Web. 02 Dec. 2009. 
<http://www.ainizetxopitea.com/link_websites/yochaos/tesis.html>. 
v Briggs. Fractals. 44. 
vi Mayer-Kress, Ph.D., Gottfried J., and Jenifer Bacon. "Collaboration: SCIENCE, ART, & CHAOS." IRIS Universe: 
44-46. Print. Number Sixteen 
vii Briggs. Fractals. 92. 
viii Briggs. Fractals. 102-103. 
ix "File:Glue1 800x600.jpg -." Wikipedia, the free encyclopedia. Web. 04 Dec. 2009. 
<http://en.wikipedia.org/wiki/File:Glue1_800x600.jpg>. 
x Pickover, Clifford A. Computers, Pattern, Chaos and Beauty Graphics from an Unseen World. Boston: St Martins 
Pr, 1991. 8-11. 
xi Briggs. Fractals. 156. 
xii Barnsley, Michael F. Fractals everywhere. Boston: Academic, 1988. Print. 87, 188.