# Animations in R

**PabRod - R**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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I’ve recently discovered the package *gganimate* thanks to this

brilliant

example.

I’ve been playing with the package during this weekend, and I created

some examples that I spread through

Twitter.

Some Twitter users showed interest in knowing more. I hope this short

tutorial can satisfy them.

## Libraries used

We’re going to need the following libraries:

# Numerical library(pracma) # To calculate the Taylor polynomials library(reshape) # For using melt # Display library(ggplot2) # For plotting library(ggthemes) # Also for plotting library(gganimate) # For animating. Install using devtools::install_github('thomasp85/gganimate') library(kableExtra) # To display nice tables

## Animating a moving particle

Here we’ll generate a moving particle. First, we need the positions in

time. In our case, the dynamical equations will be given by:

$$ \begin{cases} x(t) = cos(t) \\ y(t) = sin(2t) \end{cases}$$

So we generate the series and store them in a dataframe:

ts <- seq(0, 2*pi, length.out = 100) xs <- cos(ts) ys <- sin(2*ts) particle <- data.frame(ts = ts, xs = xs, ys = ys)

The code for generating the animation follows a very similar syntax to

*ggplot*. In this case, we indicate that the values of *ts* should be

used as the transition time.

ggplot(data = particle) + geom_point(aes(x = xs, y = ys), col = 'red') + # Generate the plot theme_tufte() + # Make ... labs(x = 'x', y = 'y') + # ... it ... scale_y_continuous(limits = c(-2, 2)) + # ... look ... guides(col = FALSE) + # ... pretty. transition_time(ts) + # And animate! ease_aes('linear')

## Animating a Taylor series

Let's see now a more complex example. Our purpose is to explore Taylor

polynomials of different degrees approximating the function

$$f(x) = cos(\frac{3x}{2}) e^{-x} $$

around a given point.

Thus, we begin creating the function:

f <- function(x) { cos(1.5*x)*exp(-x) }

In this case, we want to compare how good is the performance of Taylor

polynomials of different orders. The data we have to generate is a bit

more complex than before.

xs <- seq(-2, 2*pi, length.out = 1500) # Values of x x0 <- 1 # Value of x where the Taylor series will be centered ys <- matrix(0, nrow = length(xs), ncol = 9) for(i in 1:9) { # Extract Taylor polynomials of orders 0 to 8 order <- i - 1 # Indexes have to be positive, but first order is 0 if(order == 0) { # A Taylor polynomial of order zero is just... ys[,i] <- f(x0) # ... a constant function } else { taylor_coefs <- taylor(f = f, x0 = x0, n = order) # Get polynomial ys[,i] <- polyval(taylor_coefs, xs) # Evaluate polynomial } } # Rewrite as dataframe df <- data.frame(ys) colnames(df) <- seq(0,8) df <- melt(df) df <- cbind(df, xs = rep(xs,9), f = f(xs)) colnames(df) <- c('order', 'ys', 'xs', 'f')

The resulting dataframe is a collection of polynomials of different

orders evaluated at each point in *xs*. Additionally, we added the

values of the original function *f(x)*, also at each point:

order | ys | xs | f |
---|---|---|---|

0 | 0.0260228 | -2.000000 | -7.315110 |

0 | 0.0260228 | -1.994474 | -7.265955 |

0 | 0.0260228 | -1.988948 | -7.216622 |

0 | 0.0260228 | -1.983423 | -7.167120 |

0 | 0.0260228 | -1.977897 | -7.117454 |

0 | 0.0260228 | -1.972371 | -7.067632 |

A static plot will look like:

ggplot(data = df) + geom_point(aes(x = xs, y = ys, col = order)) + # Generate basic plot geom_point(aes(x = xs, y = f)) + # Plot also original function geom_point(aes(x = x0, y = f(x0)), col = 'black', size = 5) + # Remark initial point theme_tufte() + # Make it ... labs(x = 'x', y = 'y') + # ... look ... scale_y_continuous(limits = c(-2, 2)) # ... pretty.

In order to animate it, now we will use the command

*transition_states*, using *order* (the order of the Taylor polynomial)

as the animation parameter. The parameters *transition_length* and

*state_length* control how much time each state stays in screen, and

how long the transition between states should look.

ggplot(data = df) + geom_point(aes(x = xs, y = ys), col = 'red') + # Add basic plot geom_point(aes(x = xs, y = f)) + # Plot also original function geom_point(aes(x = x0, y = f(x0)), col = 'red', size = 5) + # Remark initial point theme_tufte() + # Make ... labs(x = 'x', y = 'y') + # ... it ... scale_y_continuous(limits = c(-2, 2)) + # ... look ... guides(col = FALSE) + # ... pretty. transition_states(order, transition_length = 1, state_length = 0.5) + # And animate! ease_aes('linear')

The result could not look nicer!

This entry appears in R-bloggers.com

PS: If you liked this post, this

visualization I made in *GeoGebra*

some time ago may also be of your interest.

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**PabRod - R**.

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