# 4d Mathmrs. Mac's Messages

This example shows several techniques to visualize four dimensional (4-D) data in MATLAB®.

### Visualize 4-D Data with One Discrete Variable

Sometimes data has a variable which is discrete with only a few possible values. You can create multiple plots of the same type for data in each discrete group. For example, use the `stem3` function to see the relationship between three variables where the fourth variable divides the population into discrete groups.

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### Visualize 4-D Data with Multiple Plots

Under Mac OS, 40 x 40 pixels; under Windows, 40 x 80 pixels; If you pass an icon with a size that is smaller than these limits, it is centered but not resized. However, when its size exceeds these limits, it is both centered and resized. Pass True in foreground when you want to force the progress window to the foreground of the application. Presenting Apple Music on Mac. The new Apple Music app is the ultimate music streaming experience on Mac. 1 Explore a library of 60 million songs, discover new artists and tracks, find the perfect playlist, download and listen offline, or enjoy all the music you’ve collected over the years.

With a large data set you might want to see if individual variables are correlated. You can use the `plotmatrix` function to create an n by n matrix of plots to see the pair-wise relationships between the variables. The `plotmatrix` function returns two outputs. The first output is a matrix of the line objects used in the scatter plots. The second is a matrix of the axes objects that are created.

The `plotmatrix` function can also be used for higher order data sets.

### Visualize Function of Three Variables

For many kinds of four dimensional data, you can use color to represent the fourth dimension. This works well if you have a function of three variables.

For example, represent highway deaths in the United States as a function of longitude, latitude, and if the location is rural or urban. The x, y, and z values in the plot represent these three variables. The color represents the number of highway deaths.

### Visualize Data in a Volume

Your data may contain a measured value for a physical object such as temperature in a pipe. In this cases, the physical dimensions can be represented as a volume with color used to represent the magnitude of the measurement. For example, use the `slice` function to show the value of the measured variable at cross-sections within the volume.

### Plot the Function of a Complex Variable

A complex function has an input with real and imaginary parts and an output with real and imaginary parts. You can use a three dimensional plot with color to represent the complex function. In this case the x and y axes represent the real and imaginary parts of the input. The z axis represents the real part of the output and the color represents the imaginary part of the output.

Catalina

macOS Catalina gives you more of everything you love about Mac. Experience music, TV, and podcasts in three all-new Mac apps. Enjoy your favorite iPad apps now on your Mac. Extend your workspace and expand your creativity with iPad and Apple Pencil. And discover smart new features in the apps you use every day. Now you can take everything you do above and beyond.

## Music, TV, and podcasts take center stage.

iTunes forever changed the way people experienced music, movies, and podcasts. It all changes again with three all-new, dedicated apps — Apple Music, Apple TV, and Apple Podcasts — each designed from the ground up to be the best way to enjoy entertainment on your Mac. And rest assured; everything you had in your iTunes library is still accessible in each app. iCloud seamlessly syncs everything across your devices — or you can back up, restore, and sync by connecting the device directly to your Mac.

### Presenting Apple Music on Mac.

The new Apple Music app is the ultimate music streaming experience on Mac.1 Explore a library of 60 million songs, discover new artists and tracks, find the perfect playlist, download and listen offline, or enjoy all the music you’ve collected over the years. And find it all in your music library on all your devices.

### Listen up. Podcasts on Mac.

The best entertainment, comedy, news, and sports shows are now available on your Mac with Apple Podcasts. Search for podcasts by title, topic, guest, host, content, and more. Subscribe and be notified as soon as new episodes become available. And in the Listen Now tab, you can easily pick up where you left off across all your devices.

## The apps you love.Right on your Mac.

Experience your favorite iPad apps now on your Mac. With Mac Catalyst, developers can easily create Mac apps from the iPad apps you already know and love. They run natively alongside your existing Mac apps so you can drag and drop content between them. They take full advantage of the larger screen and powerful architecture of your Mac. And because they are built from their iOS versions, they provide a seamless experience across your devices. Enjoy a broad range of Mac apps — from travel, entertainment, and gaming to banking, education, and project management.

The Twitter for Mac app takes full advantage of the native Mac features like multiple windows, drag and drop, keyboard shortcuts, and more. See more of what’s happening on a larger screen and easily work alongside your other Mac apps.

Morpholio Board for Mac lets interior designers create their mood boards on a larger screen with much more detail. Users can scroll through a huge library of furnishings; use new editing, composition, curation, and organization tools; and work alongside web browsers, notes, and email.

With the Post-it® App on Mac, users can easily organize all their notes on the big screen. Grouping and sorting is much faster using a keyboard and mouse or trackpad. And importing boards from other users is even easier.

With Jira for Mac, manage projects like a boss. Take advantage of native Mac features and move through Jira faster than ever, push notifications, keyboard shortcuts, drag and drop, custom menu bar, and more.

The American Airlines app for Mac lets users check in and choose their seats, see three-dimensional renderings of their seats powered by SceneKit, and even view traffic to the airport provided by Maps.

With TripIt on Mac, you can review all your plans in one place, edit and share your trip details, and research your destination, all while multitasking with other Mac apps. Your itinerary is even available offline, whether you’re at your desk or at 35,000 feet.

The Crew app for Mac is the first communications app designed for workers who don’t have easy access to communication technology on the job. Managers often use Mac computers in the back of house at stores, so users can access the experience they expect on the platform they prefer.

This popular language-learning solution opens a whole new world on Mac. The desktop is wonderfully suited for focus and learning. Rosetta Stone is tightly integrated with the Mac microphone and includes an offline mode for a seamless app experience that’s just not possible on the web.

Proloquo2Go on Mac is designed for people with communication challenges who are unable to make themselves understood using their own voices. The app lets parents, teachers, and therapists customize the app vocabulary using the keyboard and provide new words without requiring access to their child’s device, which may be at school or at home.

### Even more amazing Mac apps.Even more amazing Mac apps

Developers are continuing to build for Catalyst as many more of your favorite iPad apps will be coming to Mac.

## The apps you use every day, made extraordinary.

With macOS Catalina, the apps you love are now more beautiful and intelligent than ever. So your everyday tasks are easier than ever.

Photos has a new immersive, dynamic look that showcases your photos and memories. See only the best shots in your library, without the duplicates and clutter. Browse your favorite photos by days, months, and years and get larger previews of all your photos. And Photos is even smarter, so it can highlight important moments like birthdays, anniversaries, and trips.

Easier to find. And easier to share.

A new gallery view and more powerful search help you find your notes quicker than ever. Shared folders let you collaborate on entire folders of notes with another person or a group. And new checklist options let you move completed items to the bottom, quickly reorder items using drag and drop, and more.

Organization.
Reorganized.

The Reminders app has been completely rebuilt, with an all-new design and new ways to easily create, organize, and keep track of reminders. Add attachments to reminders, create or change reminders with the quick edit buttons, and let Siri suggest new ones found in Messages. Smart lists automatically organize and display your upcoming reminders. And if you tag someone in a reminder, you’ll be notified the next time you’re chatting in Messages.

Start browsing.
Faster.

An updated start page helps you easily and quickly access your favorites and frequently visited sites. And Siri suggestions surface bookmarks, iCloud Tabs, and links from your reading list, as well as those you receive in Messages.

#### Play extraordinary.

Try it free2

Sidecar lets you extend your workspace by using your iPad as a second Mac display.3 Work in one app while you reference another or view your artwork on your Mac while you use tools and palettes on your iPad. You can also mirror the screens so they both display the same content, making it perfect for sharing exactly what you see with others.

View the Sidecar white paper (PDF)

### Express your creativity. With Apple Pencil.

Bring the ease and precision of Apple Pencil to your favorite creative Mac apps with Sidecar.4 Just drag your app window from your Mac to your iPad as you would with any second display. Then use Apple Pencil to design in Illustrator, edit photos in Affinity Photo, or create 3D models in ZBrush. The handy sidebar puts essential Command, Control, and Shift keys right at your fingertips.

### Make your mark on Mac.

Use Apple Pencil for everyday tasks like drawing and sketching or marking up screenshots and PDFs. You can easily insert a sketch from your iPad into any document on your Mac.

### Powerful apps. Made even more powerful.

Discover all the amazing apps that are compatible with Sidecar, including illustration, photography, and 3D apps.

Affinity Photo

Maya

## Screen Time.Now on Mac.

macOS Catalina brings all your favorite Screen Time features to Mac, giving you greater insight into how you’re spending your time. Monitor usage, schedule downtime, and set limits for both apps and websites across all your devices. And with Family Sharing, you can set app and communication limits for your kids to help them focus on the right things.

### Communication Limits

Communication Limits let you choose who your children can communicate with throughout the day and during downtime, so you can make sure they’re always reachable.

### Combined Limits

With Combined Limits, you can combine individual apps and websites, and even whole categories, into a single, easy-to-manage limit. Set a limit for a group of apps and websites, like gaming or your favorite streaming apps.

### One More Minute

Need an extra minute to wrap up what you’re doing? You’ll get a notification when you’ve reached your time limit, so you can quickly wrap up a conversation, save a file, or close a game session before your time runs out.

## Increased security.Greater privacy.

With macOS Catalina, there are enhanced security features to better protect macOS against tampering, help ensure that the apps you use are safe, and give you greater control over access to your data. And it’s even easier to find your Mac if it’s lost or stolen.

### More secure hardware.

The Apple T2 Security Chip keeps your Mac secure by ensuring that you’re running trusted software and automatically encrypting your stored data. It also provides secure authentication for Touch ID. And now macOS Catalina features Activation Lock, so only you can erase and reactivate your Mac.

### Safer-running software.

macOS Catalina runs in its own read-only volume, so it’s separate from all other data on your Mac, and nothing can accidentally overwrite your system files. And Gatekeeper ensures that new apps you install have been checked for known security issues before you run them, so you’re always using good software.

### Data protections.

Apps must now get your permission before directly accessing files in your Documents and Desktop folders, iCloud Drive, and external volumes, so you’re always in control of your data. And you’ll be prompted before any app can capture keyboard activity or a photo or video of your screen.

The new Find My app combines Find My iPhone and Find My Friends into a single, easy-to-use app on Mac, iPad, and iPhone. Find My can help you locate a missing Mac — even if it’s offline and sleeping — by sending out Bluetooth signals that can be detected by Apple devices in use nearby. They can then relay the detected location of your Mac to iCloud so you can locate it in the Find My app.

It’s all anonymous and encrypted end-to-end so no one, including Apple, knows the identity of any reporting device. And because the reporting happens silently using tiny bits of data that piggyback on existing network traffic, there’s no need to worry about your battery life, your data usage, or your privacy.

## Powerful features to empower everyone.

macOS Catalina includes new features to help everyone get the most out of Mac. Tools for users with low vision allow you to zoom in on a paragraph of text or the entire screen.

### Zoom Display

If you have two screens, you can keep one screen zoomed in close while the other remains at a standard resolution. It’s great for everyday work and giving a presentation.

### Hover Text

Hover Text makes it easier to view text on your Mac display. Just hover over any text with your cursor and press Command. You’ll get a dedicated window with large, high-resolution text. You can even choose the fonts and colors.

## macOS Catalina

### The power of Mac.Taken further.

Featuring all-new, dedicated apps for music, TV, and podcasts. Smart new features in the apps you use every day. And Sidecar, which lets you use iPad as a second Mac display.

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2012 and later

2012 and later

2012 and later

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2017 and later

(all models)

2013 and later