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Paras31

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1 years, 91 days
Hellenic Open University
Mathematician

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Teacher of Mathematics with a proven track record of working in education management. Proficient in Ease of Adaptation, Course Design, and Instructional Technology. Holds a Bachelor's degree in Mathematics from the University of the Aegean and a Master's in Applied Mathematics at the Hellenic Open University, focusing on Ordinary and Partial Differential Equations. His enthusiasm lies in the application of mathematical models to real-world contexts, such as epidemiology and population growth. Aside from his passion for teaching, Athanasios enjoys football, basketball, and spending time with his dogs.

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These are questions asked by Paras31

Plotting Julia sets with Maple...

Paras31 245 Maple 2025
fractal julia plotting
April 07 2025
2 2

I am studying the Julia sets. I have tried the following two codes to generate Julia Sets. The first one I found in Maple Help, and the second one from http://ftp.informatik.rwth-aachen.de/maple/mfrjulfn.htm. I am wondering if there exists another code to generate the Julia set. My question is just for educational purposes, because those two codes work fine.
 

> 

with(Fractals:-EscapeTime); with(ImageTools); bl, ur := -2.0-1.5*I, 2.0+1.5*I; c := -1; J := Julia(700, bl, ur, c, cutoff = 4, iterationlimit = 6000, output = layer1); Embed(J)
> 

restart; julfn_zsqrd := proc (x, y) local c, z, m; c := evalf(0); z := evalf(x+I*y); for m from 0 to 50 while abs(z) < 2 do z := -z^2+z end do; m end proc; plot3d(0, -1.0 .. 2.0, -2.0 .. 2.0, style = patchnogrid, orientation = [-90, 0], grid = [250, 250], scaling = constrained, color = julfn_zsqrd)

 
> 

NULL


 

Download Julia_Sets.mw

Finding and plotting the 6th roots of un...

Paras31 245 Maple 2025
complex roots plotting
March 31 2025
3 0

I was reading a book on complex analysis, and I tried to answer some questions like "Find and plot the sixth roots of unity on Maple."  I tried the following code, which works. Is there any other way to solve and plot the same question?

> 

with(plots); interface(imaginaryunit = 'I'); s := [seq(exp(2*I*Pi*k*(1/6)), k = 0 .. 5)]; X := [seq(Re(s[k]), k = 1 .. 6)]; Y := [seq(Im(s[k]), k = 1 .. 6)]

[1, 1/2+((1/2)*I)*3^(1/2), -1/2+((1/2)*I)*3^(1/2), -1, -1/2-((1/2)*I)*3^(1/2), 1/2-((1/2)*I)*3^(1/2)]

  

[1, 1/2, -1/2, -1, -1/2, 1/2]

  

[0, (1/2)*3^(1/2), (1/2)*3^(1/2), 0, -(1/2)*3^(1/2), -(1/2)*3^(1/2)]

 (1)
> 

UnitCircle := plot([cos(t), sin(t), t = 0 .. 2*Pi], color = gray, linestyle = dash); RootsPlot := pointplot([X, Y], symbol = solidcircle, color = blue, symbolsize = 10); display(UnitCircle, RootsPlot, scaling = constrained, title = "6th Roots of Unity")

 
> 

NULL


 

Download 6th_roots_of_unity.mw

Understanding PDEs' Initial Condition ...

Paras31 245 Maple 2024
March 20 2025
2 4

All three expressions define the same initial velocity condition in different notations.
ic1 := u(x, 0) = f, D[2](u)(x, 0) = g
ic2 := u(x, 0) = f, diff(u(x, 0), t) = g;
ic3 := u(x, 0) = f, u__t(x, 0) = g;  

Why does only ic1 work while ic2 and ic3 do not? Should I use another way?

wave_equation_1D.mw

How to Create a Better Plot for Shaded ...

Paras31 245 Maple 2024
March 05 2025
2 1

Hi everyone,

I am trying to visualize the integral of x3 over the interval x=−1 to x=1. I tried using:

with(plots):
display(
   plot(x^3, x = -1 .. 1, color = black, thickness = 2),
   shadebetween(x^3, 0, x = -1 .. 1, color = cyan)
);

This works, but I wondered if there’s a better or more elegant way to visualize definite integrals. For example:

  • Can I add transparency to the shaded region?
  • Is there a built-in function that directly plots definite integrals with shading?
  • Any tips for improving the aesthetics of such plots?

Thanks in advance for any help!

Download εμβαδόν_χωρίου.mw

How to Arrange Multiple Plots in a Grid ...

Paras31 245 Maple 2024
array plotting display
December 27 2024
2 1

I am working on visualizing the results of an SIR model in Maple. I’ve created multiple plots for different parameter values using dsolve and odeplot, and I’d like to arrange them in a grid (e.g., 2 rows x 3 columns) for easier comparison. Here’s what I’ve tried:

> 

restart; with(plots); n := 10^6; s__0 := n-1; i__0 := 1; r__0 := 0; simulate_SIR := proc (beta, gamma) local lambda, sys, ic, sols, single_plot; lambda := beta*i(t)/n; sys := diff(s(t), t) = -lambda*s(t), diff(i(t), t) = lambda*s(t)-gamma*i(t), diff(r(t), t) = gamma*i(t); ic := s(0) = s__0, i(0) = i__0, r(0) = r__0; sols := dsolve({sys, ic}, numeric, output = listprocedure); single_plot := display([odeplot(sols, [t, s(t)], 0 .. 60, color = red), odeplot(sols, [t, i(t)], 0 .. 60, color = blue), odeplot(sols, [t, r(t)], 0 .. 60, color = green)], labels = ["Time [day]", "Population"], labeldirections = [horizontal, vertical], legend = ["Susceptible", "Infected", "Recovered"], legendstyle = [location = right]); return single_plot end proc; plot1 := simulate_SIR(.1, .1); plot2 := simulate_SIR(.2, .1); plot3 := simulate_SIR(.7, .1); plot4 := simulate_SIR(1.5, .1); plot5 := simulate_SIR(1, 0.25e-1); plot6 := simulate_SIR(1, .2); plot7 := simulate_SIR(1, .5); plot8 := simulate_SIR(1, 1); combined_plot := display([plot1, plot2, plot3, plot4, plot5, plot6, plot7, plot8], insequence = true, view = [0 .. 60, 0 .. n], grid = [2, 4]); combined_plot

 
 

NULL

Download grid.mw

Unfortunately, the insequence=true and gird=[2, 4] options didn’t work as I expected. Instead of arranging the plots in a grid, they appear like an animation

How can I correctly arrange multiple plots into a grid layout in Maple? Are there specific options or steps I’m missing? I would appreciate any guidance or examples.

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