Chaps13.mw

 Maple Text Commands for Chapter 13 - COMPLEX ITERATIVE MAPS 

 

Figure 13.1(a): Plotting Julia sets. 

> x1:=array(0..1000000):y1:=array(0..1000000):
k:=15:iter:=2^k:
a:=-0.5:b:=0.3:die:=rand(0..1):
x1[0]:=Re(0.5+sqrt(0.25-(a+I*b))):
y1[0]:=Im(0.5+sqrt(0.25-(a+I*b))):
2*abs(x1[0]+I*y1[0]);
for i from 0 to iter do
x:=x1[i]:y:=y1[i]:
u:=sqrt((x-a)^2+(y-b)^2)/2:v:=(x-a)/2:
u1:=evalf(sqrt(u+v)):v1:=evalf(sqrt(u-v)):
x1[i+1]:=u1:y1[i+1]:=v1:if y1[i]<b then y1[i+1]:=-y1[i+1]:fi:
die();
if (die()=0) then x1[i+1]:=-u1:y1[i+1]:=-y1[i+1]:fi:od:
m:='m':
with(plots):
pts:=[[x1[m],y1[m]] $m=0..iter]:
pointplot(pts,style=point,symbol=circle,symbolsize=1,color=black,axes=FRAMED,scaling=CONSTRAINED,font=[TIMES,ROMAN,15]);
 

2.785907878 

Plot 

Figure 13.2: The color Mandelbrot set. 

> Mandelbrot:=proc(x,y)
local c,z,m:
c:=evalf(x+y*I):z:=c:
for m to 50 while abs(z^2)<16 do z:=z^2+c end do:
m end:
with(plots):
densityplot(Mandelbrot,-2.2..0.8,-1.5..1.5,style=patchnogrid,colorstyle=HUE,grid=[300,300],axes=none);
 

Warning, the name changecoords has been redefined 

Plot 

End of Chapter 13 Commands