Question: How to animate a set of plots with changing views/axis

April 15 2014 geischtli 10
Maple

2

Hi guys!

 

I want to do a fractalzoom into the mandelbrot fractal. The basic idea was to produce all single plot pictures, and then display/animate the zoom by iterate through the list. But I cant find a solution that really works. Any help would be very appreciated :)

 

So where am I? A single picture is made like this: (Sorry math tool didnt take it)

 

plot3d(0, -2 .. 1, -1.5 .. 1.5, orientation = [-90, 0], grid = [250, 250], style = patchnogrid, color = mandelbrot, lightmodel = None):

As u can see, I use the colorfunc property to color the plane. The mandelbrot procedure evalueates how many iterations are needed to go beyond 2 (> 2).

I cant post pictures, so heres the code if u want to reproduce some:

mandelbrot := proc (x, y)

local c, z, iterationCount, position, iterations;

z := 0; iterations := 0; iterationCount := 35;

position := Complex(x, y);

c := evalf(position);

while iterations < iterationCount do

    if 2 <= abs(z) then return iterations;

    else z := z^2+c; iterations := iterations+1;

    end if

od;

return iterations

end:

 

As you can see i get a list of PLOT3D structures, each with different axis sizes or views. The problem now is when i use the straightforward way:

display(plots, insequence=true);

the animated frames get smaller and smaller, because the frame is set to the same size as the first frame. 

Do you have any idea how I can make the axis somewhat dynamic, or do you see a better approach?

 

Here's the rest of the code to produce the effect. Its nearly hardcoded, because its still in experimental phase, sorry for that :P

The test does the following: Start with window -2 .. 1, -1.5 .. 1.5 and with linear interpolation zoom in to the window -0.82 .. -0.7, -0.2 .. -0.08.

 v is used to store the view explicitely, is explained afterwards

 

steps := 3:

d1 := (2-0.82)/steps:

d2 := (1+0.7)/steps:

d3 := (1.5-0.2)/steps:

d4 := (1.5+0.08)/steps:

l := Array(1 .. 4):

v := Array(1 .. 4):

for i from 0 to steps do

    v(i+1) := [d1*i-2 .. -d2*i+1, -1.5+d3*i .. 1.5-d4*i, 0 .. 0];

    l(i+1) := plot3d(0, d1*i-2 .. -d2*i+1, -1.5+d3*i .. 1.5-d4*i, orientation = [-90, 0], grid = [100, 100], style = patchnogrid, color = mandelbrot, lightmodel = None);

od:

 

display a single picture:

display(l(4));

 

create the animation:

ll := convert(l, list):

display(ll, insequence = true);

 

Another approach:

I tried to explicitely give the view as argument:

display(l(i), view = v(i)), v(i) stored in previous render loop. This works, but then the question to resolve is how to draw each frame into the same plot figure and not creating a new plot window for each one?

 

Now you should have all informations, any help is very welcome!

Thanks in advance,

Cheers,

geischtli

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