I am using MATLAB to go through a NxN grid in the complex plane, the x's are the real component and the y's are the imaginary component. For each point on this grid I am using it as a starting point for Newton's Method. Depending on which root it converges to it is assigned a number. This number is used with pcolor to plot the fractal.
It plots nicely, however, I want to also plot the color darkness depending on how long it takes to converge to the root. I am having trouble with pcolor. I was able to get the 3 colors for the 3 roots but I am not quite sure how to add more colors so that it is more descriptive.
Here is the code to get the plot after I have
xp - array of x points
yp - array of y points
col - NxN matrix that has either 1, 2, 3 (corresponds to which root)
% thresholds for color
caxis([1 3]);
% sets colors Red, Green, Blue
mycolors = [1 0 0; 0 1 0; 0 0 1];
colormap(mycolors);
% real component on x and imaginary component on y
h=pcolor(xp, yp, col');
set(h, 'LineStyle', 'none' );
So, how can I get there to be a gradient in pcolor, it seems that pcolor just kind of figures out all the colors itself. And caxis only allows boundaries for 2 colors.
Let me know if you want to see the full code of this program.
Thank you
Add the number of iterations it took to get to convergence as a color. Define the colors in HSV, and make the number of iterations map to the value S of HSV. That will give you a nice and meaningful color gradient without really changing the colors.
The pseudocode is:
For that, generate your 3 colors mycolors as you do. Change their color space as mycolorshsv=rgb2hsv(mycolors);
What you want now is to generate a bunch (your choice) of colors per color.
mycolorshsv=repelem(mycolorshsv,N,1);
Now lets generate N gradients per color.
mycolorshsv( 1: N,2)=linspace(0,1,N);
mycolorshsv( N+1:2*N,2)=linspace(0,1,N);
mycolorshsv(2*N+1:3*N,2)=linspace(0,1,N);
You want e.g. the longest iteration you obtained maxiter to be the brightest. We need to transform your col matrix from [1,2,3] to our current range now. For that, just
col=(col-1)*N+1; % make 1=>1, 2=>N, 3=>2*N;
col=col+iteration_matrix; %max(iteration_matrix) must be maxiter. You may want to normalize so min(iteration_matrix) is 0
Now simply set the colormap(mycolors);, and I would use imagesc instead of pcolor, but its less important.
Play with the range, and limits of the colro values for nicer maps. Often non-linear maps are also used, where a function f is applied to the iteration values, such as the sigmoid.
This is the technique used for the newton fractals you can find in wikipedia, such as:
Related
I am trying to write a script to plot florescence intensity from some microscopy data as a scatter plot and threshold this data based on cells that respond greater than a certain amount in CFPMAX and plot these in green and cells that do not in red. When I try to plot this, I am unable to really assign proper colors to points and they end up being blue and red. I need each cell in the image to be assigned 4 values, (3 values for for each florescence channel and one value to determine whether or not it responded (green or red). Thus I was wondering if it was possible to assign the proper color to the 4th column of the matrix, or if I am going about this the wrong way all together. I have attached my code below.
MCHR=csvread('data1.csv');
MYFP=csvread('data2.csv');
MCFP=csvread('data3.csv');
CFPMAX=(max(MCFP))';
MCHMAX=(max(MCHR))';
YFPMAX=(max(MYFP))';
c=zeros(length(CFPMAX));
for i=1:length(c)
if CFPMAX(i)>40
c(i)='g'; %// green responders
else
c(i)='r'; %// red non-responders
end
end
MM=horzcat(MCHMAX,YFPMAX,CFPMAX,c);
scatter(MM(:,1),MM(:,2),100,MM(:,4),'filled','MarkerEdgeColor',[0 0 0])
title('Responders vs Non-Responders ')
xlabel('[TF1]') %// x-axis label
ylabel('[TF2]') %// y-axis label
As far as I can tell from the documentation, the input parameter c (assuming scatter(x,y,a,c,...)) can be one of:
A single character specifying a colour e.g. 'g' or 'r'. But just one single scalar colouring all of you points.
A single RGB triple colouring all of your points so [1,0,0] for red or [0,1,0] for green.
A three column matrix of RGB triples. This is likely what you want. I will demonstrate this to you.
A one column matrix of numbers which will colour the points according to a colormap. This one will also work for you but less explicitly. Incidentally, I would guess that this is option that MATLAB though your vector of characters was.
So in order to create the matrix of RGB triples you can modify your code to be
c=zeros(length(CFPMAX),3);
for i = 1:length(CFPMAX)
if CFPMAX(i)>40
c(i,:)=[0,1,0]; %// green responders
else
c(i,:)=[1,0,0]; %// red non-responders
end
end
However, you could actually do away with the for-loop completely in MATLAB and construct c in a vectorized approach using logical indexing:
c=zeros(length(CFPMAX),3);
c(CFPMAX > 40, 2) = 1; %// green responders
c(CFPMAX <= 40, 1) = 1; %// red responders
This is a more idiomatic way to do this in MATLAB.
So i have this code to obtain radial gravity on Earth in function of the latitude:
G=6.6e-11;
M=5.976e24;
N=1000;
r=6371000;
w=2*pi/(24*3600);
for i=1:1:360
Theta=i*pi/180;
x(i)=i;
Vi(i)=-G*M/(r*r);
Phii(i)=r*w*w*sin(Theta)*sin(Theta);
gr(i)=Vi(i)+Phii(i);
end
plot(x,gr)
And it runs well. I want to make a graph of a circle made of a border of points (representing angle (i)) that change colour according to the value of gr(I want to set ranges of values of gr so that if the value obtained falls in a specific category, the point will have a specific colour).
I'm really new to MATLAB. Is there any possible way to make this?
Thanks in advance.
Here is the basic algorithm that I would do:
Determine how many colours you want to represent in your plot.
Create a colour map that has this many points for what you want to compute.
Determine a linearly increasing vector that varies from the minimum value of gr to the maximum value of gr with as many points as you have determined in Step #2
For each point in gr:
a. Determine which point yields the closest distance of this point to the vector in Step #3
b. Use this to index which colour you want.
c. Convert your angle into Cartesian co-ordinates, then plot this point with the colour found in Step 4b.
Let's tackle each point in detail.
Step #1 - Determine how many colours you want
This is pretty simple. Just determine how many colours you want. For now, let's assume that you want 20 colours, so:
num_colours = 20;
Step #2 - Create a colour map
What we can do is create a 20 x 3 matrix where each row determines a RGB tuple that denotes the amount of red, green and blue that each colour will occupy. MATLAB has built-in colour maps that will help you facilitate this. Here are all of the available colour maps that MATLAB has:
Each colour map has a special variable where you can provide it an integer number, and it'll return this 2D matrix of as many rows as the number you have provided. Each row gives you an RGB triplet which denotes the proportion of red, green and blue respectively. This matrix varies from the beginning of the colour map (top row) to the end (bottom row). All you have to do is use any name seen in the figure I've shown you above to create a colour map of that type. For example, if you wanted to get a bones colour map of 15 points, simply do:
colour_map = bones(15);
If you wanted to get a jet colour map of 25 points, simply do:
colour_map = jet(25);
.... you get the idea right? I like hsv so let's use the HSV colour map. You can use any colour map you want, but let's just stick with HSV for the sake of this example.
As such:
colour_map = hsv(num_colours);
Step #3 - Get that linearly increasing vector
You want certain colours to map into certain ranges, which is why this step is important. Given a value in gr, we want to figure out which colour we want to choose, and all you have to do is determine which value in gr is the closest to a value in this vector in Step #3. Therefore, you can use linspace to do this for you:
bin_vector = linspace(min(gr), max(gr), num_colours);
This will create a num_colours 1D array where the beginning of this array starts at the minimum value of gr and varies up to the maximum value of gr and each value is equally spaced such that we generate a num_colours array.
Step #4 - Bring it all home
Now, for each point in gr, we need to figure out which point is the closest to that vector in Step #3, we then use this to figure out the colour we want, then we need to convert our angle into Cartesian co-ordinates, then plot this point.
For illustration purposes, I'm going to assume your radius is 1. You can figure out how to get the x and y co-ordinates by simply doing cos(theta) and sin(theta), where theta is the angle you are examining. Since your gr array has 360 slots, I'm going to assume a resolution of 1 degree per slot. Therefore, you can easily do this in a for loop. Make sure you use hold on because we are going to call plot multiple times, and we don't want to overwrite the plot each time we call plot. You want all of the points to stay in the plot.
Without further ado:
figure; %// Create blank figure
hold on; %// Remember all points
%// For each point in our array...
for idx = 1 : 360
%// Find the closest slot between gr and our vector in Step #3
[~,min_idx] = min(abs(gr(idx) - bin_vector));
%// Grab this colour
clr = colour_map(min_idx,:);
%// Plot the point with this colour
plot(cosd(idx), sind(idx), '.', 'Color', clr, 'MarkerSize', 10);
end
Take notice that cosd and sind take in degrees as the input argument while cos and sin take in radians. Also, take note that I also changed the size of the point so that it's bigger. With the above logic, and your array in gr, this is what I get:
If you want the radius to get larger, all you have to do is multiply each cosd and sind term with your radius. Therefore, you can do something like this:
radius = 2;
for idx = 1 : 360
... %// Insert colour code here
...
...
%// Now plot
plot(radius*cosd(idx), radius*sind(idx), '.', 'Color', clr, 'MarkerSize', 10);
end
Just leave the code the same, but for the plot command, just multiply each x and y value by the radius.
Minor note in efficiency
The way you're calculating your gr array is using an inefficient for loop. There are some situations (like mine above) where you need to use a for loop, but for simple computations there is no need. It's better if you vectorize its creation. Therefore, you can get rid of the for loop to calculate your gr array like so:
x = 1 : 360;
Theta = x*pi/180;
Phii = r*w*w*sin(Theta).*sin(Theta);
Vi = -G*M/(r*r);
gr = Vi + Phii;
x is simply a vector going from 1 to 360, and that's done in the first line. Also, Vi is just an array which contains a single value and if you know how operations work between a scalar and an array, you can just do an addition with this single value and it'll add every value in your array by this much. As such, there's no need to create an array for Vi. Also, take a look at how I calculated Phii. I'm using element-by-element operations as Theta is now an array. You want to create an array Phii that takes corresponding values of Theta, and applies that formula to each value in Theta to produce Phii.
Hope this helps. Good luck!
I have 11 1x50 matrices that contain densities. The first looks like [20, 20, 20... 20] and represents time=0. The second looks like [20, 19, 22,..], etc. and represents time=100. These continue to vary until t=1000.
What I'm hoping to do is to create a plot with the elements' position on the x-axis (50 positions for the 50 pieces of data in each) and time (0-1000) on the y-axis. Ideally, I'd like the plot to be completely filled in with color densities, and a colorbar on the side that shows what densities the color range represents.
Any help would be greatly appreciated!
Sort of inspired by: http://www.chrisstucchio.com/blog/2012/dont_use_scatterplots.html
Assuming you have (or can arrange to have) all those vectors as columns of a 11x50 matrix:
A = randi(100, 11,50); %//example data
you can just use
imagesc(1:50, 0:100:1000, A)
colorbar
axis xy %// y axis increasing, not decreasing
Example:
Looking at the comments, it will be easier to stack these vectors into a 2D matrix. You have 11 individually named vectors. Assuming that your vectors are named vec1, vec2, vec3, etc., create a 2D matrix A that stacks these vectors on top of each other. Also, you'll need to include an extra row and column at the end of this matrix that contains the minimum over all of your vectors. The reason why this is will be apparent later, but for now take my word for it as this is what you need.
In other words:
A = [vec1; vec2; vec3; vec4; vec5; vec6; vec7; vec8; ...
vec9; vec10; vec11];
minA = min(A(:));
A = [A minA*ones(11,1); minA*ones(1,51)];
As such, the first row contains the information at time 0, the next row contains information at time 100, etc. up to time 1000.
Now that we have that finished, we can use the pcolor function to plot this data for you. pcolor stands for pseudo-coloured checkerboard plot. You call this by doing:
pcolor(A);
This will take a matrix stored in A and produce a checkerboard plot of your data. Each point in your matrix gets assigned a colour. The colours get automatically mapped so that the least value gets mapped to the lowest colour while the highest value gets mapped to the highest colour. pcolor does not plot the last row and last column of the matrix, but pcolor does use all of the data in the matrix. In order to ensure that the colours get properly mapped, we need to pad your matrix so that the last row and last column get assigned to the smallest value over all of your vectors. As you want to plot all values in the matrix, that's why we did what we did above.
Once we do this, we'll need to modify the X and Y ticks so that it conforms to your data. As such:
pcolor(A);
set(gca, 'XTick', 0.5:5:51.5);
set(gca, 'XTickLabel', 0:5:50);
set(gca, 'YTick', 1.5:11.5);
set(gca, 'YTickLabel', 0:100:1000);
xlabel('Sample Number');
ylabel('Time');
colorbar;
What the code does above is that it generates a checkerboard pattern like what we talked about. This labels the Sample Number on the x axis while time is on the y axis. You'll see with the two set commands that I did, this is a bit of a hack. The y axis by default labeled the ticks going from 1 - 12. What I did was that I changed these labels so that they go from 0 to 1000 in steps of 100 instead and I also removed the tick of 12. In addition, I have made sure that these labels go in the middle of each row. I do this by setting the YTick property so that I add 0.5 to each value going from 1 - 11. Once I do this, I then change the labels so that they go from 0 - 1000 in steps of 100. I also do the same for the x axis in a similar fashion to the y axis. I then add a colorbar to the side as per your request.
Following the above code, and generating random integer data that is between 13 and 27 as per your comments:
A = randi([13,27], 11, 50);
minA = min(A(:));
A = [A minA*ones(11,1); minA*ones(1,51)];
We get:
Obviously, the limits of the colour bar will change depending on the dynamic range of your data. I used randi and generated random integers within the range of 13 to 27. When you use this code for your purposes, the range of the colour bar will change depending on the dynamic range of your data, but the colours will be adjusted accordingly.
Good luck!
In a 3D scatter graph of MATLAB I have 15 different clusters of data that I want to highlight. I can see MATLAB has 8 specific colors. Is there any other way I could use 7 more colors just to distinguish the clusters?
Thanks
I would recommend to use this File Exchange submission - Generate maximally perceptually-distinct colors
It allows you to create a colormap with very distinguished colors and apply them with COLORMAP function. See help for this submission for more options.
colors = distinguishable_colors(n_colors);
For 3D scatter you can use this colors as an argument (C) in SCATTER3:
scatter3(X,Y,Z,[],colors)
To use this colors for different lines set them as default color order either for current figure:
set(gcf,'DefaultAxesColorOrder',colors)
or all figures:
set(0,'DefaultAxesColorOrder',colors
You can use the color property using set. You must first get a handle h to the drawing objects and set(h,'color',[0.2 0.3 0.9]). The color is rgb ranging from 0 to 1 for each channel.
From the Matlab documentation:
scatter(X,Y,S,C) displays colored circles at the locations specified
by the vectors X and Y (which must be the same size).
S determines the area of each marker (specified in points^2). S can be
a vector the same length as X and Y or a scalar. If S is a scalar,
MATLAB draws all the markers the same size. If S is empty, the default
size is used.
C determines the color of each marker. When C is a vector the same
length as X and Y, the values in C are linearly mapped to the colors
in the current colormap. When C is a 1-by-3 matrix, it specifies the
colors of the markers as RGB values. If you have 3 points in the
scatter plot and wish to have the colors be indices into the colormap,
C should be a 3-by-1 matrix. C can also be a color string (see
ColorSpec for a list of color string specifiers).
So, for example, say that your clusters are given by the columns of the matrices X and Y, with the k'th column being the k'th cluster, X being the X coordinates, and Y being the Y coordinates. We can do what you want as follows:
% make some random data in clusters:
n = 15;
m = 42;
X = 0.2*rand(m,n) + repmat(rand(1,n),m,1);
Y = 0.2*rand(m,n) + repmat(rand(1,n),m,1);
% lets change the colour map:
colormap(jet);
% now plot each, one at a time, and each with a different colour:
hold on;
for k=1:n
scatter(X(:,k),Y(:,k),40,k/n*ones(m,1));
end
If you don't like these colours, you can change the colormap, and if you don't like the color maps, you can, as the other answer points out, insert any RGB values you want.
I am trying to plot a matrix where each element is in one out of two states. (ising model..)
Now, I would like to have one state colored and the other one white. That works using
[i,j] = find(S);
figure(gcf);
plothandle = scatter(i,j);
axis([0 nNodes+1 0 nNodes+1]);
when S holds the Spins and one state is equal to 0. (find returns a matrix of only non-zero elements)
To have a useful plot, the sizes of the markers should be 1x1 in RELATIVE coordinates. So if the whole matrix S would be in a state non-zero, everything would be colored.
However, it seems like Matlab only allows MarkerSizes in points or inches. How could I solve this?
One idea I had was, that I find out the point-size of the axes and then can easily calculate how big my markers should be. Then I would have to create a callback function if I want to zoom in and so on. Also, I have not yet found a way (without the image acq. toolbox) to find out the absolute size of my axes.
To clarify what I want: How could I plot a chessboard using a matrix with 1 for black and 0 for white fields?
For displaying data of this sort I generally prefer IMAGE or IMAGESC to PCOLOR since PCOLOR won't display the last row and column of the matrix when using faceted shading (the default). Also, IMAGE and IMAGESC flip the y axis so the image more intuitively matches what you think of when looking at a matrix (i.e. rows start from 1 at the top). You can visualize your matrix like this:
S = round(rand(20)); %# Sample 20-by-20 matrix of ones and zeroes
imagesc(S); %# Plot the image
colormap([1 1 1; 0 0 0]); %# Set the colormap to show white (zero elements) and
%# black (non-zero elements)
And here's a sample image:
Just as a suggestion, you can try using pcolor instead of `scatter' Example:
pcolor(hadamard(20))
colormap(gray(2))
axis ij
axis square