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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

Hello,

can I remove tick marks from axis in plots ?

Hi,

thank for any  help.

I need you help to make a movies ( animation)  according to the index k=1..10.  k is used in Vect_T[k], vector of time to make an animation of the true solution, and it's also used in Matrix(M[..,..,k]), h

True solution:ow can I make a seq of plots for different value of k. 

 

plot3d(True_solution(x,y,Vect_T[k]),x=0..a,y=0..b,axes=boxed,grid= [11,11]);

Analytic solution

plots:-matrixplot(Matrix(M[..,..,k]),axes=boxed,tickmarks= [[1="0", 2=" ", 3=" ", 4=" ", 5=".4", 6=" ", 7=" 0.6", 8=" ", 9=".8", 10=" ", 11="1"],[1="0", 2=" ", 3=" ", 4=" ", 5=".4", 6=" ", 7=" 0.6", 8=" ", 9=".8", 10=" ", 11="1"],default],labels=[x,y,u],axes = boxed);

I tried, this:

S:=seq(plots:-matrixplot(Matrix(M[..,..,i]),labels=[x,y,u],axes = boxed),i=1..10):
plots:-display(S);
 But I get only one figure.

 also,

I tried

BoxTrue:=Null;
for k from 1 to 10 do
BoxTrue:=BoxTrue, plot3d(True_solution(x,y,Vector_time[k]),x=0..a,y=0..b,axes=boxed,grid= [11,11]): od:
display(BoxTrue, insequence=true);
also, no display

 

restart:with(plots):

h3:=((1+lambda*m*x/a0+phi*((4/Pi*sum((-1)^(n+1)/(2*n-1)*cos(2*Pi*(2*n-1)*x),n=1..infinity)))));

q:=Q-1:

f:=sin(alpha)/E;

DP3:=Int(f-((q*(k+1)*(k+2))/((1-tau)^(k+1)*((h3^(k+2)))*(k+1+tau)))^(1/k),x=0..1);

E:=0.2:phi:=0.2:alpha:=0.1:k:=1:lambda:=0.1:a0:=0.5:m:=0.1:tau:=0.1:

plot((DP3),Q=0..1,axes=box,linestyle=1,color=[red]);

I am unable to plot DP3 vs Q, not only it take very long time but didn't give any output.

Please have a look.

 

Cheers!

 

Pls, I tried solving the system of PDE numerically.... When I did for just 1 plot, the graph was plotted easilyrunning.mw but When I varied some parameters its not coming out.... Also, its not bringing any error so I can't trace out my mistakes....Not_runnin.mw PLS HELP ME OUT with the multiple plots... Attached are my source codes links....

 

I have created a diagram with "plots" and "plottools" that involves the line command creating a line in 3-space.  It works just fine on all of my machines and versions of Maple but it fails on Maple 17 in the Windows 8 environment.   By "fai;s" I mean that it does not draw the line; it does not generate an error message.   Any idea what's happening? 

Dear Primers,

 

I am new to Maple and want to ask how to merge two point plots. Suppose, I have two different point plots with same x coordinates but varying y coordinates. How can I merge them just like you would merge two different line plots on a single graph?

 

Please keep it simple thanks.

Hi,

I tried to create a graph with two different x-axes and y-axes, for example:

It's no doubt that we can use the "dualaxisplot" to generated a plot with two different y-axes as follows:

 

 

It's seem that Maple can realize plots with two different x-axes , because some of cases present functions through upper x-axis, such as:

 

How should I create a graph to display functions using the bottom and left sides as the x- and y-axis for one, and the top and right sides as the x- and y-axis for the other?

I'd appreciate any help on this topic. Thank a lot.

 

if statment plot...

December 19 2013 m-Dede 10

> restart;

> with(plots):

> dp := proc(X,Y)

>     X[1]*Y[1]+X[2]*Y[2];

> end:

> nrm := proc(X)

>     sqrt(dp(X,X));

> end:

> r:=[3*cos(u),3*sin(u)];

> lambda:=1;

>  f:=proc(X)

> local Xu,s,T,N,kappa,v,n,pr,v1,z;

> Xu := [diff(X[1],u),diff(X[2],u)];

> s := nrm(Xu);

> T:=[diff(X[1],u)/s,diff(X[2],u)/s];

> N:=[-T[2],T[1]];

> kappa:=simplify(dp(diff(T,u),N))/s;

> v:=int(kappa,u=0..u);

> z:=v;

> if z=0 then -1 else  v1:=z fi;

> n:=[cos(v1)*N[1]+sin(v1)*T[1],cos(v1)*N[2]+sin(v1)*T[2]];

> pr:=([r[1]+lambda*n[1],r[2]+lambda*n[2]]);

> end:

> plot([f(r)[1],f(r)[2],-18..18]);

 

can you please help me , I'm not sure what is going wrong.

Hi, i am trying to export the following bifurcation diagram into a pdf.

 

Digits:=20: N:=10000: M:=100: x_max:=1: r_min:=0:
r_max:=4: for n from 0 to N do r:=r_min+n/N*(r_max-r_min):
x:=evalf(x_max*rand()/10^12):for m from 0 to M do x:=x*exp(r*(1 - x)): od:
X[n]:=x: od:
with(plots):
bifpoint:={seq([r_min+j/N*(r_max-r_min),X[j]],j=0..N)}:
pitchf:=pointplot(bifpoint,symbol=point):display(pitchf);

 

For some reason the graph is just blank, with just the axis when i export to pdf.

Hermite Polynomial...

December 16 2013 abbeykabir 40
Hello, please i would like someone to please explain Hermite Polynomial for me. I have zero knowledge of this and if possible give examples and references. Also, on how to Normalize Hermite Polynomial and Ortogonarity of Hermite Polynomial. Thanks

Hello fellow Maple users. 
I have been useing Maple for 5 month now and i think its a great program. But sometimes i find it a bit difficult to use. 
When i plot a function i would like to see the function on the line in the plot that represents the funtion. So if have several lines representing different functions, i would Maple to highlight the function when i hower over the function 
with the mouse .. Is this posible ? I know its posible in Inspires CAS. 

It must be posible for Maple to label the plots with the function ??? If not Maple programmers got a job...

I used implitplot to plot solutions to some (tricky) equations in 2 variables, of the form implicitplot([f(x,y)=0]).  Now I have a (tricky) change of parameterization G:R^2->R^2 of the form G(x,y)=(g(x,y),h(x,y)). I'd like to plot the image of the solution set of f(x,y)=0 under the map G. Of course, if I could invert G I'd implicitplot           G^(-1)(f(x,y))=0, but the functions I have dont lend themselves to this.

 

Presumably MAPLE stores the points it plots somewhere, and I should be able to apply G to this set of points. But I don't know how to approach this. Anybody know? 

Hi there,

i want to generate some plots in files in this example:


this code doesn't work. but without restart; it works fine. i passed 2 days to figure out that "restart;" was the problem.

my questions are :

1. why i have to eliminate the first line of restart;

2. how can i save my files in a directory that is in the current directory. For example i have a directory in current directory named "plotFILES".

thanks in advance for your help

Hello,

I am solving eq1 and then plot it using odeplot. Then I am extracting data from odeplot using op[1,1]. From that I only care about  one point so I am using pt[1] := dt[1]([1, 2]); then I ploted it using pointplot. I run a do loop and at the end I am ploting all the points.

My code works fine but I am trying to have a line contacting each points. I tried  style=line but it did not work.

How can I have a line contacting each points on my final plot (which is display([pl[1], seq(allpl[k], k = 1 .. 3)])) ?

This is my code:

> restart; with(DEtools); with(plots);
> with(DEtools); with(plots);
> A := 0.2e-1; B := 10^(-5); k := 0;
> eq1 := diff(X(t), t) = -(A+B*X(t))*X(t);

> ic[1] := X(365*k) = 1000;
> s[1] := dsolve({eq1, ic[1]}, X(t), range = 0 .. .365, numeric);
> p[1] := odeplot(s[1], [[t, X(t)]], t = 0 .. .365);
> dt[1] := op([1, 1], p[1]);
> pt[1] := dt[1]([1, 2]);
> pl[1] := pointplot(pt[1], axes = boxed);
> for k to 3 do
tk := 365*k;
A := rhs(s[k](tk)[2]);
ic[k+1] := X(tk) = 500.*A;
s[k+1] := dsolve({eq1, ic[k+1]}, X(t), range = tk .. 2*tk, numeric);
p[k+1] := odeplot(s[k+1], [[t, X(t)]], t = tk .. 2*tk);
dt[k+1] := op([1, 1], p[k+1]);
pt[k+1] := dt[k+1]([1, 2]);
pl[k+1] := pointplot(pt[k+1], axes = boxed);
allpl[k] := display([pl[k+1]])
end do;
> display([pl[1], seq(allpl[k], k = 1 .. 3)]);

 

Thank you

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