Maple 9 Learning Guide - Maplesoft

150 • Chapter 5: PlottingNote: On some computers, the numpoints options value may need tobe decreased to generate the plot.1. Dirichlet Problem for a Circle> with(plots):> setoptions3d(scaling=constrained, projection=0.5,> style=patchnogrid):> f1 := (x, y) -> 0.5*sin(10*x*y):> f2 := t -> f1(cos(t), sin(t)):> a0 := evalf(Int(f2(t), t=-Pi..Pi)/Pi):> a := seq(evalf(Int(f2(t)*cos(n*t), t=-Pi..Pi)/Pi), n=1..50):> b := seq(evalf(Int(f2(t)*sin(n*t), t=-Pi..Pi)/Pi), n=1..50):> L := (r, s) -> a0/2+sum(’r^n*(a[n]*cos(n*s)+b[n]*sin(n*s))’,> ’n’=1..50):> q := plot3d([r*cos(s), r*sin(s), L(r, s)], r=0..1, s=0..2*Pi,> color=[L(r, s), -L(r, s), 0.2], grid=[29, 100],> numpoints=10000):> p := tubeplot([cos(t), sin(t), f2(t), t=-Pi..Pi,> radius=0.015], tubepoints=70, numpoints=1500):> display3d({q, p}, orientation=[3, 89], lightmodel=light3);2. Mandelbrot SetThe Mandelbrot Set is one of the most complex objects in mathematicsgiven the chaotic nature that surrounds the image. Code for thisgraphic is available at the Maple Application Center.3. Origami BirdThe Origami Bird can be displayed as a simple graphic as well as aMaple animation. Code for the graphic and the animation are availableat the Maple Application Center.4. ConchoidCode for this and other seashells is available at the Maple ApplicationCenter.5. Gauss Map Graphed on a Torus> with(plots):> sp := [rho*cos(2*Pi*t), rho*sin(2*Pi*t), 0, radius=b]:> pc := n -> [ (rho-r*cos(2*Pi*t))*cos(2*Pi/(n+t)),> (rho-r*cos(2*Pi*t))*sin(2*Pi/(n+t)),> -r*sin(2*Pi*t)]:> rho, r, b := 3, 1.1, 1:> s := spacecurve( {seq(pc(k), k=1..50)}, t=0..1, thickness=2,> color=blue, view=[-4.4..4.4, -4.4..4.4, -2.2..2.2]):> s2 := tubeplot( sp, t=0..1, tubepoints=150,> view=[-4.4..4.4, -4.4..4.4, -2.2..2.2], style=PATCHNOGRID,> color=cyan):