/Mrs.,

How can I plot "log scale base 2" instead of "log scale base 10" (plot "log2plot(x,x=0..10)" instead of "logplot(x,x=0..10)")? 

I would appreciate if you make me some help with this situation.

faithfully,

Download spatial_1.mw

Download spatial_1.mw

Dear friends,

I have a given number and I need to convert its digits into an array. For example: 

a:= 456;  and I need an array [4 5 6]. 

I know how to obtain such a procedure as a list

map(parse, StringTools:-Explode(convert(a, string)));

but not how to get the result as an array. Could you please help me with the right commands?

Many thanks for the help. 

Download Transition_Probaility_Markov_chain.mw

How to find sgn on maple?

signum.mw

Hi, I'm solving a complicated ODEs. It is a multiple point bvp. Last time I asked a question about a similar problem(you can see https://www.mapleprimes.com/questions/230626-I-Am-Trying-To-Solve-A-Set-Of-ODEs-With). And when I use the last point 's solution to obtain the next point's solution (via approxsoln=..), it works well (it's the replicate of other people's paper). But this time I changed theoretical model, so the input parameters and the equations are some different from the previous. Some problems appears again. In the code I used a loop to calculate solutions with different lambda, but the code works on some points in front, then it appears an error "initial Newton iteration is not converging". 

Do you have some ideas to overcome it?

dsolveODEs.mw

How to evaluate the integration when ?

integration_24sep.mw

I am trying to solve a set of ODEs with dsolve. There are 26 equations of my ODEs, but the problem is a multiple point bvp. So the range is divided into three region. In order to use dsolve, I transform the three subregion's coordinate into 0 to 1. Meanwhile, the ODEs are different in three regions, respectively. So, there are 26×3 equations in total. And according to the paper I want to replicate, it says the response is unstable,so parameter continuation is used. Similar to the paper, an additional equation is added(eq1_27 in code), also an additional condition is added(about lambda). When the lambda is less then 0.11, the dsolve works, but for other values it doesn't work. Could anyone help me?

Sorry for the tedious programming code, I am new to Maple.

I am trying to reproduce this fractal graphic by Daniel Geisler, using maple 18:

http://tetration.org/Tetration/index.html

I suspect the images were produced by fractint - with a floating point hardware accelerator, but I am not sure. In any case, they were produced by a numerical program, not a symbolic one and probably with 16-18 digits of accuracy.

The Maple code I use makes for a valiant effort, but is nowhere close in accuracy to the two images above. Here's the Maple 18 code:

tetrationFractal18.mw

Several questions here:

1) Geisler's image colors according to period (right graph). Period 1 is red. 2 is yellow (although not all yellow regions are period 2) 3 is green, 4 is cyan, 5 is blue, etc.

I have some period checking code in my doc, which stores the last 20 iterates of the maxIter iterations of the orbit in orb[n]  then extracts a period p, based on some backwards comparisons.

I am only interested in graphing max period up to N=20, hence the orb[1..N] array, stores only the last N elements of the iterates. This is relatively fast, but extracting the period (below) from the orb array, puts an additional strain on the overall calculations, probably of the order of O((N+p)*n) for each n in the iteration, where p is the period returned. That's why I avoid storing in orb unless the global bound "bail" has not been exceeded.

The period finding algorithm works. It rerurns p correctly, and that's the value the graphic proc returns for plot3d. The problem is that the range of values is small (p\in[1..N]) and therefore the palette in plot3d is poor. I.e., it doesn't differentiate very much between colors of different period regions. How can I spread out the color pallete with plot3d with such results? ideally, I'd like to assign colors roughly from red to violet, with period 1 red, 2 orange, 3 green, 4 blue, 5 purple, etc.

I tried returning log(p) and this spreads the zhue some, but not enough (see attached document). Further, I'd like to assign black to points which escape the calculations, such as when the bail bound is exceeded in my iteration loop. By default, these show up as "purple", which is the same as the color for period 1 with the latest implementation. How can I except these escape points from the palette, i.e. what does the fractal proc have to return to color these black? Note that for these points, orb[n] defaults to 0, so the palette colors this close to p=1 region (these are the black "hairs"/threads of the Cantor Bouquets in Geisler's second image. That's the first question.

Second question is, why are there "white" regions interlaced under this scheme? is the calculation failing at these points because of low resolution? (epsilon~0.01 in this doc). (If points fail "bound"=1e10 then the orbit is orb[1..N]=0, so p=1 and zhue=1?) White seems to decrease as I increase epsilon and maxIter, but i can't test further, because the calculation limit is already prohibitive for this version of Maple. The graph with a plot3d grid [400,400] and maxIter=100 and epsilon=0.01, takes around 25 minutes. Testing anything finer than than, is time uneasonable.

Would increasing Digits help with any of the above?

Does anyone have any ideas on how to improve the code performance for this graph in maple 18, as per the above problems?.

Many thanks.

I would like to "run" or execute parts of my code that I put in a same section. Unfortunately, selecting "Execute" when right-clicking on a section does nothing...

I created some simple maple 9 code to do some z->w mappings long time ago, on my web page:

https://ingalidakis.com/math/ComplexMaps.html

Upon revising my webpage, I've stumbled upon a page for comformal mappings, by David Bau:

http://davidbau.com/conformal/#exp(z)

Here's the current version of my code in Maple 18:

rrestart;
NULL;
with(plots);
xMax := 1;
yMax := 1;
N := 10;
step := abs(xMax)/N;
GL := proc (x, y) options operator, arrow; x+I*y end proc;
f := sin;
G := {};
for k from -N+1 to N+1 do

G := `union`(G, {complexplot(f(GL(x, (k-1)*step)), x = -xMax .. xMax, color = brown)});

G := `union`(G, {complexplot(f(GL((k-1)*step, y)), y = -yMax .. yMax, color = brown)})

end do;
display(G, scaling = constrained);

The code is pretty simple: I am simply scanning the 1x1 unit square complex grid and create a complex plot of it on the w-plane, by passing it through whatever function is at: f:=x.

Does anyone have any idea why the grid lines on the w-plane do not agree with Bau's grid lines mapping of the w-plane? To try it for exp for example, input "exp(z)" in Bau's home page.

The difference is quite noticeable, especially on exp and log, where the orientation of the w-grid on the left and right half-planes, seem to be opposite of what my code displays.

The reason may be Mathematical, but from what I see from the description on Bau's page, there's no difference on the identity function, so I am clueless.

Many thanks in advance

Hi guys,

an error appeared in solving a set of equations and plotting the solution, I dont know how to handle it!!

Thanks for your help

Best

problem.mw

Download 01.mw01.mw

i don't know why it doesn't work now.Please help
 

Download ask_maple.mw