Removing vertical lines in a piecewise function when discontinuty points are not known

I am creating various cantor staircases by starting from different functions:

for example:

N = 3;
f{1} = @(x)sin(2*pi*x);
for i = 1:N-1
    f{i+1} = @(x)(0.5*f{i}(3*x).*(x<=1/3) + 0.5.*(x>1/3 & x<2/3) + (0.5+0.5*f{i}(3*x-2)).*(x>=2/3 & x <=1));
end
x = linspace(0,1,1000);
plot(x,f{N}(x))

The problem is that vertical lines are emerging.

How do I remove the vertical lines when I do not know(do not want to find) the discontinuity points? Surely there has to be a way...

[Catalytic]

Surely there has to be a way...

Why?

Answer 1

[Torsten]

Maybe something like this. But the jump height of 0.05 at discontinuities most probably has to be adjusted in other applications.

N = 3;
f{1} = @(x)sin(2*pi*x);
for i = 1:N-1
    f{i+1} = @(x)(0.5*f{i}(3*x).*(x<=1/3) + 0.5.*(x>1/3 & x<2/3) + (0.5+0.5*f{i}(3*x-2)).*(x>=2/3 & x <=1));
end
x = linspace(0,1,1000);
y = f{N}(x);

idx = find(abs(diff(y)) > 0.05);
idx(end+1) = numel(x);
hold on
iend = 0;
for i = 1:numel(idx)
  istart = iend + 1;
  iend = idx(i);
  plot(x(istart:iend),y(istart:iend),'b');
end
hold off
grid on

[Vivaan]

Is it possible to store this function in a variable somehow?

[Torsten]

You can save the separate "sections" of the x- and y-array in a cell array. This cell array will have elements equal to the number of sections. In the loop, you can add the two lines

X_array{i} = x(istart:iend);
Y_array{i} = y(istart:iend);

before or after the plot command.

Answer 2

[chicken vector]

EDIT: Thanks to @Torsten

figure;
tiledlayout(2,2);

for N = 2 : 5
    nexttile;
    f{1} = @(x)sin(2*pi*x);
    for i = 1 : N-1
        f{i+1} = @(x)(0.5*f{i}(3*x).*(x<=1/3) + 0.5.*(x>1/3 & x<2/3) + (0.5+0.5*f{i}(3*x-2)).*(x>=2/3 & x <=1));
    end
    x = linspace(0,1,1000);
    y = f{N}(x);
    horizontalIdx = [diff(y)~=0, 1];
    breakIdx = [1 strfind([0 horizontalIdx 0], [1 0])];
    hold on;
    for line = 1 : length(breakIdx)-1
        idx = breakIdx(line):breakIdx(line+1)-1;
        plot(x(idx), y(idx),'Color',[0 0.4470 0.7410]);
    end
    hold off;
    box on;
end

OLD ANSWER:

I am assuming you meant horizontal lines as I don't see any vertical ones.

N = 3;
f{1} = @(x)sin(2*pi*x);
for i = 1:N-1
    f{i+1} = @(x)(0.5*f{i}(3*x).*(x<=1/3) + 0.5.*(x>1/3 & x<2/3) + (0.5+0.5*f{i}(3*x-2)).*(x>=2/3 & x <=1));
end
x = linspace(0,1,1000);
y = f{N}(x);

You can use:

horizontalIdx = find([diff(y)==0, 0]);
y(horizontalIdx) = NaN;
figure;
plot(x,y);

Or:

horizontalIdx = [diff(y)~=0, 0];
startIdx = strfind([0 horizontalIdx], [0 1]) + 1;
endIdx = strfind([horizontalIdx 0], [1 0]);

figure;
hold on;
for line = 1 : length(startIdx)
    idx = startIdx(line):endIdx(line);
    plot(x(idx), y(idx),'Color',[0 0.4470 0.7410]);
end
hold off;
box on;

[Torsten]

I am assuming you meant horizontal lines as I don't see any vertical ones.

No, @Vivaan meant the graph at discontinuities, thus where wrong vertical lines appear.

[chicken vector]

You are right, I was completely blind to those.