Drawing a Koch Curve with MAPLE

[Soff]

I try to create my first program with MAPLE! Therefore, I really need your help!
I'd like to draw a Koch curve with the two function f and d and a constant a=0.5+sqrt(3)/6 *I.

Koch curve:=proc(x,y);

local a ,d, f,m;
z:=evalf(x+y*I);
a := 1/2+sqrt(3)/6*I;

d :=a*conjugate(z) ;
f:=a+(1-a)*conjugate(z) ;

m:=0; to 40 while abs(z)<1 do z:=d..f;
m:=m+1;
od m

end:
plot(Koch curve);

However, I know, I'm not very good at programming because it's the first time I do something like this. Can someone give me some advices? What's wrong with the program above? I think there are lots of errors, but can anyone help me? I really want to learn it!

 

[Soff]

Okay, I know, I did it totally wrong. However, I tried again and used this time the program Mathematica:

z := 1 + 2*I
x = 1/1000
a := 1/2 + Sqrt[3]/6*I
Element[b, {0, 1}]
Array[Solve[x = Sum[b/2\^k, k, {1, 10}], b], 1000]

Plot[Re[If[b = 0, a*Conjugate[z], a + (1 - a)*Conjugate[z]]],
Im[If[b = 0, a*Conjugate[z], a + (1 - a)*Conjugate[z]]]]

But program above doesn't work. But I'm getting closer to the solution! In case I find the solution to this problem, I will post it!

 

[tacman]

Hi there, first of all, congratulations on taking the initiative to learn a new programming language and trying to create your first program with MAPLE! It can be challenging at first, but with practice and patience, you will get the hang of it.

Now, let's take a look at your program. It looks like you have the right idea in terms of using the two functions f and d to create the Koch curve. However, there are a few things that need to be fixed.

Firstly, the line "local a,d,f,m;" declares local variables that will be used within the procedure. However, you have already declared the variable "a" in the line above. This can cause confusion and lead to errors. It would be better to just declare the variable "m" as it is the only one being used within the procedure.

Secondly, the line "z:=evalf(x+y*I);" creates a complex number using the values of x and y. This is not necessary for creating the Koch curve and can be removed.

Next, the line "d:=a*conjugate(z);" and "f:=a+(1-a)*conjugate(z);" are not using the variables "d" and "f" that you have declared earlier. Instead, they are creating new variables with the same name. To use the previously declared variables, you can use the assignment operator ":=" instead of "=".

Lastly, in the while loop, you are using the ".." operator which is used for creating ranges. To iterate through a loop, you need to use the "do" and "end do" keywords. Also, the condition for the while loop should be based on the value of "m" instead of the absolute value of "z".

Taking all of these into consideration, your program should look something like this:

KochCurve := proc(x, y)
local a, d, f, m;
a := 0.5 + sqrt(3)/6 * I;
d := a * conjugate(x + y * I);
f := a + (1-a) * conjugate(x + y * I);
m := 0;
do while m < 40
x := d;
y := f;
m := m + 1;
end do;
plot([x, y], color = blue);
end proc;

To use this procedure, you can