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I know we have all been in that all-too-common situation of needing to inefficiently identify prime numbers using only a regular expression... and now Matt Parker from Standup Maths helpfully released a YouTube video entitled "How on Earth does ^.?$|^(..+?)\1+$ produce primes?" in which he explains a simple regular expression (aka Halloween incantation) which matches composite numbers:
Here is my first attempt using MATLAB and Matt Parker's example values:
fnh = @(n) isempty(regexp(repelem('*',n),'^.?$|^(..+?)\1+$','emptymatch'));
fnh(13)
fnh(15)
fnh(101)
fnh(1000)
Feel free to try/modify the incantation yourself. Happy Halloween!
It's frustrating when a long function or script runs and prints unexpected outputs to the command window. The line producing those outputs can be difficult to find.
Run this line of code before running the script or function. Execution will pause when the line is hit and the file will open to that line. Outputs that are intentionaly displayed by functions such as disp() or fprintf() will be ignored.
dbstop if unsuppressed output
To turn this off,
dbclear if unsuppressed output
Time to time I need to filll an existing array with NaNs using logical indexing. A trick I discover is using arithmetics rather than filling. It is quite faster in some circumtances
A=rand(10000);
b=A>0.5;
tic; A(b) = NaN; toc
tic; A = A + 0./~b; toc;
If you know trick for other value filling feel free to post.
I have one question.
Would it be possible to purchase Matlab for our company and incorporate the functions provided by this software into our in-house developed software to offer it to customers? Is this kind of action permitted under the license terms? I would appreciate advice from someone knowledgeable on this matter.
Inspired by the suggestion of Mr. Chen Lin (MathWorks), I am writing this post with a humble and friendly intent to share some fascinating insights and knowledge about the Schwarzschild radius. My entry, which is related to this post, is named: 'Into the Abyss - Schwarzschild Radius (a time lapse)'.
The Schwarzschild radius (or gravitational radius) defines the radius of the event horizon of a black hole, which is the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole. This concept comes from the Schwarzschild solution to Einstein’s field equations in general relativity. Black holes are regions of spacetime where gravitational collapse has caused matter to be concentrated within such a small volume that the escape velocity exceeds the speed of light.
This is a rudimentary scientific post, as the matter of Schwarzschild radius - it's true meaning and function, is a much, much, much-more complex "thing" (not known to us entierly, by the third degre of epistemological explanation(s)).
And, very important is to mention: I am NOT an expert - by any means, on this topic, just a very curious guy, in almost anything, that has to do with science.
Schwarzschild Radius (Gravitational Radius)
The Schwarzschild radius (Rₛ) is the critical radius at which an object of mass 
must be compressed to form a black hole, specifically, a non-rotating, uncharged black hole, known as a Schwarzschild black hole. The Schwarzschild radius 
is given by the formula: 
.
must be compressed to form a black hole, specifically, a non-rotating, uncharged black hole, known as a Schwarzschild black hole. The Schwarzschild radius is given by the formula: . Where: 
.
. Key Characteristics are, that for any mass, if that mass is compressed within a sphere with radius equal to 
, the gravitational field is so strong that not even light can escape, thus forming a black hole. The Schwarzschild radius is proportional to the mass. Larger masses have larger Schwarzschild radii.
, the gravitational field is so strong that not even light can escape, thus forming a black hole. The Schwarzschild radius is proportional to the mass. Larger masses have larger Schwarzschild radii.Example:
For the Sun 
: 
.
: .So, if the Sun were compressed into a sphere with a radius of ~3 km, it would become a black hole!
Stellar-mass Black Holes form from the collapse of massive stars (roughly 
). Their Schwarzschild radius ranges from a few kilometers to tens of kilometers.
). Their Schwarzschild radius ranges from a few kilometers to tens of kilometers. Supermassive Black Holes found at the centers of galaxies, such as Sagittarius A in the Milky Way (
), their Schwarzschild radii span from a few million to billions of kilometers!
), their Schwarzschild radii span from a few million to billions of kilometers! Primordial or Micro Black Holes, are the hypothetical small black holes with masses much smaller than stellar masses, where the Schwarzschild radius could be extremely tiny.
A black hole, in general, is a solution to Einstein’s general theory of relativity where spacetime is curved to such an extent that nothing within a certain region, called the event horizon, can escape.
Types of Black Holes:
1. Schwarzschild (Non-rotating, Uncharged):
- This is the simplest type of black hole, described by the Schwarzschild solution.
- Its key feature is the singularity at the center, where the curvature of spacetime becomes infinite.
- No charge, no angular momentum (spin), and spherical symmetry.
2. Kerr (Rotating):
- Describes rotating black holes.
- Involves an additional parameter called angular momentum.
- Has an event horizon and an inner boundary, known as the ergosphere, where spacetime is dragged around by the black hole's rotation.
3. Reissner–Nordström (Charged, Non-rotating):
- A black hole with electric charge.
- A charged black hole has two event horizons (inner and outer) and a central singularity.
4. Kerr–Newman (Rotating and Charged):
- The most general solution, describing a black hole that has both charge and angular momentum.
Relationship Between Schwarzschild Radius and Black Holes
Formation of Black Holes: When a massive star exhausts its nuclear fuel, gravitational collapse can compress the core beyond the Schwarzschild radius, creating a black hole.
Event Horizon: The Schwarzschild radius marks the event horizon for a non-rotating black hole. This is the boundary beyond which no information or matter can escape the black hole.
Curvature of Spacetime: At distances closer than the Schwarzschild radius, spacetime curvature becomes so extreme that all paths, even those of light, are bent towards the black hole’s singularity.
BTW, the term singularity, scientificaly 😊, means that: we do not have a clue what is really happening right there...
Detailed Properties of Black Holes:
a. Singularity:
At the center of a black hole, within the Schwarzschild radius, lies the singularity, a point (or ring in the case of rotating black holes) where gravitational forces compress matter to infinite density and spacetime curvature becomes infinite. General relativity breaks down at the singularity, and a quantum theory of gravity is required for a complete understanding.
b. Event Horizon:
The event horizon is not a physical surface but a boundary where the escape velocity equals the speed of light. For an outside observer, objects falling into a black hole appear to slow down and fade away near the event horizon due to gravitational time dilation, a prediction of general relativity. From the perspective of the infalling object, however, it crosses the event horizon in finite time without noticing anything special at the moment of crossing.
c. Hawking Radiation: (In the post, I told that there is no radiation - to make it simple, although, there is a relatively newly-found (theoretically) radiation. Truth to be said, some physicists are still chalenging this notion, in some of it's parts...)
Quantum mechanical effects near the event horizon predict that black holes can emit radiation (Hawking radiation), a process through which black holes can lose mass and, over very long timescales, potentially evaporate completely. This process has a temperature inversely proportional to the black hole's mass, making large black holes emit extremely weak radiation. (Very trivialy speaking: the concept supposes that an anti-particle is drawn from the vakum and is anihilated with the black's hole matter (particle), and in the process, the black hole looses mass gradually and proportionally to the released energy - very slowly(!)).
This radiation is significant only for small black holes.
Gravitational Time Dilation (here, as well, things become 'super-weird'...)
Near the Schwarzschild radius, the intense gravitational field leads to time dilation. For an external observer far from the black hole, time appears to slow down for an object moving toward the event horizon. As it approaches the Schwarzschild radius, time dilation becomes so extreme that the object appears frozen in time at the horizon.
The time dilation factor is given by: 
Eg. Approaching the Schwarzschild radius and theoretically remaining just outside of it for a few hours would correspond to the passage of approximately several decades on Earth due to relativistic time dilation.
Using relativistic equations, it's estimated that near the event horizon 2 hours (120 minutes) near the black hole Sagittarius A* (as already mentioned ~ 4 million 
) - in the center of our galaxy Milky Way, could correspond to 83 years passing on Earth! However, this varies based on the precise distance from the event horizon (give or take, a decade 😬).
) - in the center of our galaxy Milky Way, could correspond to 83 years passing on Earth! However, this varies based on the precise distance from the event horizon (give or take, a decade 😬).Information Paradox (definte answer on this question, 'hold's the keys of the universe' 😊, maybe...)
The black hole information paradox arises from the seeming contradiction between general relativity and quantum mechanics.
According to quantum mechanics, information cannot be destroyed, yet anything falling into a black hole seems to be lost beyond the event horizon. Hawking radiation, which allows a black hole to evaporate, does not appear to carry information about the matter that fell into the black hole, leading to ongoing debates and research into how information is preserved in the context of black holes, or not...!
Schwarzschild Radius is the key parameter defining the size of the event horizon of a non-rotating black hole. Black Holes are regions where the Schwarzschild radius constrains all physical phenomena due to extreme gravitational forces, forming event horizons and singularities. The interaction between general relativity and quantum mechanics in the context of black holes (e.g., Hawking radiation and the information paradox) remains one of the most intriguing areas in modern theoretical physics.
For detailed and further reading: https://www.sciencedirect.com/topics/physics-and-astronomy/hawking-radiation.
I hope you will find this post, and information provided, interesting.
This year's MATLAB Shorts Mini Hack contest has kicked off, and there are already lots of interesting entries. The contest features creating a 96-frame, 4-second animation, which is looped 3 times to compose a 12-second short movie. There is an option to add audio to enhance the animation, and it's restricted to a an upper limit of 2,000 characters to promote efficient coding.
Many of the contestants have already realized the potential for creating a seamless loop, which provides a smooth transition and avoids any discontinuities when the animation is repeated. There are several ways to achieve this. An efficient method for example is utilizing sinusoidal functions, which are periodic, meaning that they repeat themselves over time:
An intuitive example of a seamless loop is @Edgar Guevara's EKG pulse entry, which features an electrocardiogram signal on an oscilloscope. The animation is perfectly matched by the audio, as explained in their post.
Another, rather sophisticated approach is featured in @Tim's Moonrun animation in last year's contest. This seamless loop is achieved by cleverly manipulating the camera position and target over a periodic spatial domain, producing this stunning result:
This essentially tells us that for a seamless loop in the spatial domain, the first frame must match the last frame (with a single timestep difference to be more precise, more on that later). But surely this cannot be achieved by zooming in, unless you are simulating a fractal. Well, there are always workarounds.
One way to achieve this is by zooming into a section that contains the first frame of the animation. This is featured in my Winter Loop entry. This is a remix of @Oliver Jaros's Winter entry, which was selected as a one of the weekly winners in the nature & space category for Week 1. The code was modified to lower the character count, but all credits for the original idea and graphics go to them. I also drew inspiration from one of my favourite games of all time, Super Mario 64. Oliver's animation reminded me of the Cool, Cool Mountain level of the game. In the game, you can enter various levels by jumping into paintings serving as portals.
This inspired the idea of zooming into a rectangular photograph frame containing the first frame of the animation to facilitate restarting the loop. One could argue that it would probably take a crazy person to have a photo of their house framed inside their own house. Well, in this economy and with the current house prices, I don't think this scenario is too far-fetched:
The implementation for this in 2-D is rather simple. Essentially, a second axes is used as the photograph. This is an efficient way of neatly updating the graphics while zooming in. The way this was implemented is explained in the following code snippet, which is a slight modification of the code in the entry:
m = 96; % Number of frames
% Axes limits for the first frame
xm = [xm1,xm2];
ym = [ym1,ym2];
% Axes limits for the last frame (photograph frame edges)
xf = [xf1,xf2];
yf = [yf1,yf2];
% Zoom-in vectors
x1 = linspace(xm(1),xf(1),m+1); % Axes left edge to left photo frame edge
x2 = linspace(xm(2),xf(2),m+1); % Axes right edge to right photo frame edge
y1 = linspace(ym(1),yf(1),m+1); % Axes bottom edge to bottom photo frame edge
y2 = linspace(ym(2),yf(2),m+1); % Axes top edge to top photo frame edge
if f==1
axis([x1(f),x2(f),y1(f),y2(f)]); % Set main axes limits
ax2 = copyobj(gca,gcf); % Create axes for the photo frame containing the first frame graphics objects
end
axis([x1(f+1),x2(f+1),y1(f+1),y2(f+1)]); % Zoom in main axes
lims = axis; % Main axes updated limits
pos = get(gca,'Position'); % Main axes position
% This keeps the relative position of the 2 axes constant:
pos = [pos(1)+diff([lims(1),xf(1)])/diff(lims(1:2))*pos(3),...
pos(2)+diff([lims(3),yf(1)])/diff(lims(3:4))*pos(4),...
diff(xf)/diff(lims(1:2))*pos(3),...
diff(yf)/diff(lims(3:4))*pos(4)];
ax2.Position = pos; % Adjust the relative position
Let's break down the code to explain the process:
- m is the total number of frames in the animation, i.e. 96 frames.
- xm & ym are the main axes limits for frame 1.
- xf & yf are the main axes limits for frame 96, corresponding to the photograph frame's edges.
- x1, x2, y1 & y2 are the zoom-in vectors, linearly spaced from the left, right, bottom & top main axes edges to the corresponding photograph edges. You have probably noticed that these contain m+1=97 points, which is 1 more than the total number of frames. This is done so that the first frame of the animation and the contents of the photograph frame are offset by a single timestep, so that there are no overlapping frames when the animation is looped, thus creating a perfect, seamless loop. That means that the first frame of the animation will contain the main axes zoomed-in by a single timestep, while the last frame of the animation (i.e. the zoomed-in photograph frame) will contain the most zoomed-out version of the graphics. This neatly wraps the animation, and displays the full zoomed-out view when the video stops playing.
- The photograph frame axes are created when f==1 (after setting the initial axes limits) by using the immensely useful copyobj function. This one-liner creates axes containing all graphics objects for the first frame.
- Zooming in on the main axes is then achieved by adjusting the limits using axis([x1(f+1),x2(f+1),y1(f+1),y2(f+1)]). The main axes current limits and position are then saved using the variables lims and pos respectively, in order to adjust the position of the photograph frame axes.
- While zooming in, it's important that the relative position of the 2 axes is kept constant. This is achieved by simply adjusting the position of the photograph frame axes at every frame, by calculating their relative ratios using the abovementioned formula. The first 2 arguments correspond to the (normalized) x and y positions of the lower left corner of the axes, while the third and fourth arguments correspond to the (normalized) width and height respectively. While this formula will work for any position of the main axes, it's a good idea to set the position as set(gca,'Position',[0 0 1 1]) for this contest, in order to take full advantage of the whole allocated window for the animation.
- Finally, note that the graphics are updated for the main axes only, and the above process is repeated for each frame until fully zooming into the photograph frame's axes.
Some of the most curious minds might wonder that while this is well and all with using the second axes to simulate the photograph, what happens to the photograph inside the photograph (and so on...)? Well, the beauty of this method is that you can repeat this as many times as necessary (just apply the formula using the current position and limits of the second axes to adjust the position of the third axes and so on). Given the speed of the animation and the very small size of the photograph inside the photograph, it would be very unlikely that you would need more than 3 axes, but the process is always good to know.
This is the final result:
I hope you found these tips useful and I'm looking forward to seeing many creative seamless loop animations in the contest.
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Here presented MATLAB code is designed to create a seamless loop animation that visualizes an isosurface derived from random data.
This entry, titled "The Scrambled Predator's Cube", builds upon my previous work and has been adapted to include dynamic elements.
In this explanation, I will break down the relatively short code, making it accessible whether you are a beginner in MATLAB or an experienced user. Let's go through the MATLAB code step by step to understand each line in detail.
Code Breakdown
d = rand(8,8,8);
Random Data Generation: This line creates a three-dimensional array d with dimensions 8×8×8 filled with random values. The rand function generates values uniformly distributed in the interval (0,1). This array serves as the input data for generating the isosurface.
iv = .5 + (f / 10000);
Isovalue Calculation: Here, the isovalue iv is computed based on the frame number f. The expression f / 10000 causes iv to increase very slowly as f increments. Starting from 0.50, this means that for every increment of f, iv changes slightly (specifically, by 0.0001). This gradual increase creates a smooth transition effect in the isosurface over time, making it look dynamic as the animation progresses.
h = patch(isosurface(d, iv), 'FaceColor', 'blue', 'EdgeColor', 'none');
Isosurface Creation: The isosurface function extracts a 3D surface from the data array d at the specified isovalue iv. The result is a patch object h that represents the isosurface in the 3D plot. The 'FaceColor', 'blue' argument sets the face color of the surface to blue, while 'EdgeColor', 'none' specifies that no edges should be drawn, giving the surface a solid appearance.
isonormals(d, h);
Surface Normals Calculation: This function calculates the normals at each vertex of the isosurface h, based on the data in d. Normals are vectors perpendicular to the surface at each point and are crucial for proper lighting calculations. By using isonormals, the appearance of depth and texture is enhanced, allowing the lighting to interact more realistically with the surface.
patch(isocaps(d, iv), 'FaceColor', 'interp', 'EdgeColor', 'none');
Isocaps Visualization: The isocaps function creates flat surfaces (caps) at the boundaries of the isosurface where the data values meet the isovalue iv. The resulting caps are then rendered as patches with 'FaceColor', 'interp', meaning the colors of the caps are interpolated based on the data values. The caps provide a more complete visual representation of the isosurface, improving its overall appearance.
colormap hsv;
Color Map Setup: This line sets the colormap of the current figure to HSV (Hue, Saturation, Value). The HSV colormap allows for a wide range of colors, which can enhance the visual appeal of the rendering by mapping different values in the data to different colors.
daspect([1, 1, 1]);
Aspect Ratio Setting: The daspect function sets the data aspect ratio of the plot to be equal in all three dimensions. This means that one unit in the x-direction is the same length as one unit in the y-direction and z-direction, ensuring that the visual representation of the 3D data is not distorted.
axis tight;
Tight Axis Setting: This command adjusts the limits of the axes so that they fit tightly around the data, removing any excess white space. It helps to focus the viewer's attention on the isosurface and related visual elements.
view(3);
3D View Configuration: The view(3) command sets the current view to a 3D perspective, allowing the viewer to see the structure of the isosurface from an angle that reveals its three-dimensional nature.
camlight right;
camlight left;
Lighting Effects: These commands add two light sources to the scene, positioned to the right and left of the view. The additional lighting enhances the shading and depth perception of the isosurface, making it appear more three-dimensional and visually appealing.
axis off;
Hide Axes: This command turns off the display of the axes in the plot. Removing the axes provides a cleaner visual representation, allowing the viewer to focus solely on the isosurface and its lighting effects without distraction from the grid lines or axis labels.
lighting phong;
Lighting Model: This line sets the lighting model to Phong. The Phong model is widely used in computer graphics as it provides smooth shading and realistic reflections. It calculates how light interacts with surfaces, enhancing the overall appearance by creating a more natural look.
This code creates a visually dynamic and appealing representation of an isosurface derived from random data. The gradual change in the isovalue allows for smooth transitions, while the combination of lighting, colors, and shading contributes to a rich 3D visualization. Each component plays a vital role in rendering the final output, showcasing advanced techniques in data visualization using MATLAB.
I'd like to share some tips about the 2024 mini hack contest, specifically related to audio:
- First (and most important), credit your source: unless you are composing your own audio, I think it's important to give credit to the original sources. It is a little sad to see several contributions with an empty line:
'Cite your audio source here (if applicable):'
- A great place to get royalty-free and high-quality music and audio (among other media) is https://pixabay.com. Be sure to check it out! I used one of their audio clips in my submission EKG pulse
- The right music can enhance the overall experience of your animation. Sometimes getting the animation to match the music beat can be hard. I suggest you try the other way around: get your music/sound effects to match the animation rhythm with a little editing. A free audio editor with many capabilities (more than enough for this contest, I think) is https://www.audacityteam.org/
- Choose a 4-second audio clip with a consistent tempo and seamless loop points, ensuring it complements your animation's mood and loops smoothly over 12 seconds without abrupt changes.
I think that when the right music is paired with the right animation, it can create a more impactful experience.
Well, this is my first time to participate in such community competitions and guess what, I've gone for 4 submissions so far (Feels Great!!)
So I wanna share some tricks that I followed for my first submission named Happy Shaping' ( Go Check it out!!):
1. Dynamic Background Color Change:
- Technique: The background color of the figure window is gradually changed using sine and cosine functions.
- Reason: These trigonometric functions (sin and cos) create smooth, oscillating transitions over time, which gives a fluid effect to the background's color shift.
- Implementation:
Color = [0.1 + 0.5*abs(sin(f/10)), 0.1 + 0.5*abs(cos(f/15)), 0.9 -
0.5*abs(sin(f/20))];
- Benefit: This introduces a smooth, visually appealing animation effect.
2. Smooth Object Motion Using Sine and Cosine:
- Technique: The position and shape of objects are based on trigonometric functions.
- Reason: Using sin(t) and cos(t) ensures that the movement is circular or elliptical, creating continuous and natural motion in animations.
- Implementation (for object position):
x = 10 * cos(t * 2 * pi) * (1 + 0.5 * sin(t * pi));
y = 10 * sin(t * 2 * pi) * (1 + 0.5 * cos(t * pi));
- Benefit: Circular and smooth motions are pleasing and easily controlled by tweaking the frequency and phase of sine/cosine functions.
3. Polygon Shape Changing Over Time:
- Technique: The number of sides of the polygon (sides) changes dynamically based on t.
- Reason: It creates variation in shape, maintaining user interest as the shape transitions from a triangle to a hexagon.
- Implementation:
sides = 3 + round(3 * abs(sin(t)));
- Benefit: This provides dynamic shape transitions over time, keeping the animation non-static.
4. Use of the fill Function for Color-Filled Shapes:
- Technique: The fill function is used to draw a polygon with smoothly changing colors.
- Reason: Filling polygons with varying colors based on time (t) allows for continuous color transitions, adding more complexity to the animation.
- Implementation:
fill(xp, yp, c, 'EdgeColor', 'none');
- Benefit: Combining both color changes and shape changes enhances the visual impact.
5. Consistent Use of hold on and hold off:
- Technique: hold on allows multiple graphic objects to be drawn on the same axes without clearing previous objects.
- Reason: This is crucial for drawing multiple elements (like polygons, circles, and lines) on the same figure.
- Benefit: It helps manage and layer different graphical elements effectively within the same frame.
6. Use of rectangle for a Smooth Ball Motion:
- Technique: The ball's motion is defined by rectangle with a Curvature of [1, 1] to make it circular.
- Reason: Using the rectangle function simplifies the process of drawing a filled circle, and controlling its position and size is intuitive.
- Benefit: It provides a straightforward way to animate circular objects within the plot.
7. Animating the Connection Line:
- Technique: A white dashed line (w--) is drawn between the polygon and the moving ball to show a connection between these objects.
- Reason: This adds interactivity to the scene, as it gives the impression that the polygon and the ball are related or connected in some way.
- Implementation:
plot([x bx], [y by], 'w--', 'LineWidth', 2);
- Benefit: A dynamic element that adds depth and narrative to the animation, guiding the viewer’s attention.
8. Frame Synchronization with Time (f and t):
- Technique: The variable f is used as a frame number, while t = f / 24 creates a link between frame and time.
- Reason: Ensuring smooth and continuous transitions in the animation over time is critical, so f acts as the control for time-based changes in shape, color, and position.
- Benefit: This makes it easy to manage frame rates and time-based updates for the animation.
If you like them, please feel free to use them for free.
function drawframe(f)
% Create a figure
figure;
hold on;
axis equal;
axis off;
% Draw the roads
rectangle('Position', [0, 0, 2, 30], 'FaceColor', [0.5 0.5 0.5]); % Left road
rectangle('Position', [2, 0, 2, 30], 'FaceColor', [0.5 0.5 0.5]); % Right road
% Draw the traffic light
trafficLightPole = rectangle('Position', [-1, 20, 1, 0.2], 'FaceColor', 'black'); % Pole
redLight = rectangle('Position', [0, 20, 0.5, 1], 'FaceColor', 'red'); % Red light
yellowLight = rectangle('Position', [0.5, 20, 0.5, 1], 'FaceColor', 'black'); % Yellow light
greenLight = rectangle('Position', [1, 20, 0.5, 1], 'FaceColor', 'black'); % Green light
carBody = rectangle('Position', [2.5, 2, 1, 4], 'Curvature', 0.2, 'FaceColor', 'red'); % Body
leftWheel = rectangle('Position', [2.5, 3.0, 0.2, 0.2], 'Curvature', [1, 1], 'FaceColor', 'black'); % Left wheel
rightWheel = rectangle('Position', [3.3, 3.0, 0.2, 0.2], 'Curvature', [1, 1], 'FaceColor', 'black'); % Right wheel
leftFrontWheel = rectangle('Position', [2.5, 5.0, 0.2, 0.2], 'Curvature', [1, 1], 'FaceColor', 'black'); % Left wheel
rightFrontWheel = rectangle('Position', [3.3, 5.0, 0.2, 0.2], 'Curvature', [1, 1], 'FaceColor', 'black'); % Right wheel
% Set limits
xlim([-1, 8]);
ylim([-1, 35]);
% Animation parameters
carSpeed = 0.5; % Speed of the car
carPosition = 2; % Initial car position
stopPosition = 15; % Position to stop at the traffic light
isStopped = false; % Car is not stopped initially
%Animation loop
for t = 1:100
% Update traffic light: Red for 40 frames, yellow for 10 frames Green for 40 frames
if t <= 40
% Red light on, yellow and green off
set(redLight, 'FaceColor', 'red');
set(yellowLight, 'FaceColor', 'black');
set(greenLight, 'FaceColor', 'black');
elseif t > 40 && t <= 50
% Change to green light
set(redLight, 'FaceColor', 'black');
set(yellowLight, 'FaceColor', 'yellow');
set(greenLight, 'FaceColor', 'black');
else
% Back to red light
set(redLight, 'FaceColor', 'black');
set(yellowLight, 'FaceColor', 'black');
set(greenLight, 'FaceColor', 'green');
isStopped = false; % Allow car to move
end
%Move the car
if ~isStopped
carPosition = carPosition + carSpeed; % Move forward
if carPosition < stopPosition
%do nothing
else
isStopped = true;
end
else
% Gradually stop the car when red
if carPosition > stopPosition
carPosition = carPosition + carSpeed*(1-t/50); % Move backward until it reaches the stop position
end
end
if carPosition >= 25
carPosition = 25;
end
% Update car position
% set(carBody, 'Position', [carPosition, 2, 1, 0.5]);
set(carBody, 'Position', [2.5, carPosition, 1, 4]);
%set(carWindow, 'Position', [carPosition + 0.2, 2.4, 0.6, 0.2]);
%set(leftWheel, 'Position', [carPosition, 1.5, 0.2, 0.2]);
set(leftWheel, 'Position', [2.5, carPosition+1, 0.2, 0.2]);
% set(rightWheel, 'Position', [carPosition + 0.8, 1.5, 0.2, 0.2]);
set(rightWheel, 'Position', [3.3, carPosition+1, 0.2, 0.2]);
set(leftFrontWheel, 'Position', [2.5, carPosition+3, 0.2, 0.2]);
set(rightFrontWheel, 'Position', [3.3, carPosition+3, 0.2, 0.2]);
% Pause to control animation speed
pause(0.01);
end
hold off;
Try to install MATLAB2024a on Ubuntu24.04. In the image below, the button indicated by the green arrow is clickable, while the button indicated by the red arrow are unclickable, and input field where text cannot be entered, preventing the installation.
Let's say you have a chance to ask the MATLAB leadership team any question. What would you ask them?
If I go to a paint store, I can get foldout color charts/swatches for every brand of paint. I can make a selection and it will tell me the exact proportions of each of base color to add to a can of white paint. There doesn't seem to be any equivalent in MATLAB. The common word "swatch" doesn't even exist in the documentation. (?) One thinks pcolor() would be the way to go about this, but pcolor documentation is the most abstruse in all of the documentation. Thanks 1e+06 !
What is the side-effect of counting the number of Deep Learning Toolbox™ updates in the last 5 years? The industry has slowly stabilised and matured, so updates have slowed down in the last 1 year, and there has been no exponential growth.Is it correct to assume that? Let's see what you think!
releaseNumNames = "R"+string(2019:2024)+["a";"b"];
releaseNumNames = releaseNumNames(:);
numReleaseNotes = [10,14,27,39,38,43,53,52,55,57,46,46];
exampleNums = [nan,nan,nan,nan,nan,nan,40,24,22,31,24,38];
bar(releaseNumNames,[numReleaseNotes;exampleNums]')
legend(["#release notes","#new/update examples"],Location="northwest")
title("Number of Deep Learning Toolbox™ update items in the last 5 years")
ylabel("#release notes")
As pointed out in Doxygen comments in code generated with Simulink Embedded Coder - MATLAB Answers - MATLAB Central (mathworks.com), it would be nice that Embedded Coder has an option to generate Doxygen-style comments for signals of buses, i.e.:
/** @brief <Signal desciption here> **/
This would allow static analysis tools to parse the comments. Please add that feature!
See the attached PDF for a higher resolution
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