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Case 1 Here, a = –0.99, and we consider the cases b = 1 and b = 0.98. The
starting point coordinates are (4, 0). See Figure 2.2. This case can be viewed
by editing and executing the following script M-file:

for n=1:12000
a=-0.99;b1=1;b2=0.98;
x1(1)=4;y1(1)=0;x2(1)=4;y2(1)=0;
x1(n+1)=b1*y1(n)+a*x1(n)+2*(1-a)*(x1(n))^2/(1+
(x1(n)^2));
y1(n+1)=-x1(n)+a*x1(n+1)+2*(1-a)*(x1(n+1)^2)/(1+
(x1(n+1)^2));
x2(n+1)=b2*y2(n)+a*x2(n)+2*(1-a)*(x2(n))^2/(1+
(x2(n)^2));
y2(n+1)=-x2(n)+a*x2(n+1)+2*(1-a)*(x2(n+1)^2)/(1+
(x2(n+1)^2));
end
subplot(2,1,1); plot(x1,y1,'.')
title('a=-0.99 b=1')
subplot(2,1,2); plot(x2,y2,'.')
title('a=-0.99 b=0.98')

Case 2 Here, a = 0.7, and we consider the cases b = 1 and b = 0.9998. The
starting point coordinates are (0, 12.1). See Figure 2.3.

In-Class Exercise

Pb. 2.23 Manifest the computer artist inside yourself. Generate new geo-
metrical morphologies, in Mira’s model, by new choices of the parameters
(–1 < a < 1 and b ≈ 1) and of the starting point. You can start with:

a b b (,
x y )
1 2 1 1
− 048. 1 093. ( 4 0, )
− 025. 1 099. ( 3 0, )
01. 1 0 99. ( 3 0, )
0 5. 1 0 9998. ( 3 0, )
0 99. 1 0 9998. ( 0 12, )

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