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A clip of an animation project made in Scratch.

An
**
animation project
**
is a
project
that generally consists of a sequence of images of the motion of objects to create a video. On
Scratch
, users make short movies, music videos, comical shorts, and more through a variety of techniques. Animation can involve programming
sprites
to , move, and interact. Sometimes, programmers may use animations as tutorials to show others how to do something. Sometimes animations use little to no programming and consist of a sequence of images played in consecutive order quickly. Scratch provides the project creator with the freedom to make an animation in any desired manner.

An animated sprite lip syncing to a song.

Lip syncing involves moving a mouth at the right timing of the sound. Many animations have this feature. Realistic and perfect lip sync is very complicated to reproduce as mouth shapes need to be recorded. A trick that a lot of animators use is making a sprite with different costumes, all different mouth shapes, and then using the
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block in between costume changes. A list can also be used, containing the amount of time to wait before switching to the next costume to reduce block clutter.

Outside of Scratch, lip syncing generally refers to when a musical artist's microphone is turned off yet they sing the song to their own prerecorded vocals. Likewise, if the singer's mouth replicates the vocals simultaneously being played out of the speakers, it is considered to be well-done lip syncing.

Scratch has the capabilities to animate the mouth based on the volume input of a project viewer's microphone. The loudness block takes a constant measurement of 0-100 representing the volume of the sound input. If the loudness value is higher, a costume with a more opened mouth can be switched to. A custom block to animate a mouth based on the volume input is as follows:

A walk cycle is an animation of some character walking. Sometimes the background scrolls in a loop, too, to make it seem like the character is actually displacing. The most common method is to have a sequence of costumes in which the sprite rapidly and continually switches to the . When it gets to the end, it switches back to the first costume. Because of this, the last costume needs to lead into the first costume to make the walk cycle continuous.

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who writes for
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, is a practical guide on visualization and how to approach real-world data. The book is published by Wiley and is available
on Amazon
and other major online booksellers.

**
Introduction
**

Chapter 1 —
**
Telling Stories with Data
**

Chapter 2 —
**
Handling Data
**

Chapter 3 —
**
Choosing Tools to Visualize Data
**

Chapter 4 —
**
Visualizing Patterns over Time
**

Chapter 5 —
**
Visualizing Proportions
**

Chapter 6 —
**
Visualizing Relationships
**

Chapter 7 —
**
Spotting Differences
**

Chapter 8 —
**
Visualizing Spatial Relationships
**

Chapter 9 —
**
Designing with a Purpose
**

There are lots of books on visualization that describe best practices and design concepts, but what do you do when it comes time for you to actually make something?

If you don't know how to use the software in front of you, the abstract isn't all that useful. And with growing amounts of data, it's becoming more important to be able to make sense of and communicate with it all.

In
*
Visualize This
*
, Nathan Yau teaches you how to create graphics that tell stories with real data, and you'll have fun in the process. Learn to make statistical graphics in R, design in Illustrator, and create interactive graphics in JavaScript and Flash Actionscript.

Yau draws from his experience as a graduate student in statistics and his work with major news organizations for an engaging, data-first approach. After all, visualization is about the data it's based on.

Chapters group examples and tutorials by data type and take you through the process of data exploration and analysis, to visuals, and finally, to a graphic that is fit for publication for print and online.

Read the book cover-to-cover, or keep it on your desk as a reference for your data projects. Pages are in full color with tons of graphics to inspire and to help you learn visually.

"Even better than the blog, if that's possible."

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: @flowingdata has produced an incredible book called Visualize This. If you like data visualization, go and get it:
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: The @FlowingData book has arrived! Even better than the blog, if that's possible.

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Now let’s use Theano for a slightly more sophisticated task: create a function which computes the derivative of some expression
*
y
*
with respect to its parameter
*
x
*
. To do this we will use the macro
```
T.grad
```

. For instance, we can compute the gradient of with respect to . Note that: .

Here is the code to compute this gradient:

In this example, we can see from
```
pp(gy)
```

that we are computing the correct symbolic gradient.
```
fill((x
**
2),
1.0)
```

means to make a matrix of the same shape as
*
x
*
**
*
2
*
and fill it with
*
1.0
*
.

The optimizer simplifies the symbolic gradient expression. You can see this by digging inside the internal properties of the compiled function.

After optimization there is only one Apply node left in the graph, which doubles the input.

We can also compute the gradient of complex expressions such as the logistic function defined above. It turns out that the derivative of the logistic is: .

A plot of the gradient of the logistic function, with on the x-axis and on the y-axis.

In general, for any
**
scalar
**
expression
*
s
*
,
```
T.grad(s,
w)
```

provides the Theano expression for computing . In this way Theano can be used for doing
**
efficient
**
symbolic differentiation (as the expression returned by
```
T.grad
```

will be optimized during compilation), even for function with many inputs. (see
automatic differentiation
for a description of symbolic differentiation).

Note

The second argument of can be a list, in which case the output is also a list. The order in both lists is important: element of the output list is the gradient of the first argument of with respect to the -th element of the list given as second argument. The first argument of has to be a scalar (a tensor of size 1). For more information on the semantics of the arguments of and details about the implementation, see this section of the library.

Additional information on the inner workings of differentiation may also be found in the more advanced tutorial Extending Theano .

In Theano’s parlance, the term
*
Jacobian
*
designates the tensor comprising the first partial derivatives of the output of a function with respect to its inputs. (This is a generalization of to the so-called Jacobian matrix in Mathematics.) Theano implements the
```
theano.gradient.jacobian()
```

macro that does all that is needed to compute the Jacobian. The following text explains how to do it manually.

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