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R is a programming language for
statistical computing Computational statistics, or statistical computing, is the bond between statistics and computer science. It means statistical methods that are enabled by using computational methods. It is the area of computational science (or scientific computin ...
and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners,
bioinformaticians Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combine ...
and
statistician A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may wor ...
s for
data analysis Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, enco ...
and developing
statistical software Statistical software are specialized computer programs for analysis in statistics and econometrics. Open-source * ADaMSoft – a generalized statistical software with data mining algorithms and methods for data management * ADMB – a software ...
. Users have created packages to augment the functions of the R language. According to user surveys and studies of scholarly literature databases, R is one of the most commonly used programming languages used in data mining. R ranks 12th in the TIOBE index, a measure of programming language popularity, in which the language peaked in 8th place in August 2020. The official R software environment is an open-source free software environment within the GNU package, available under the GNU General Public License. It is written primarily in C, Fortran, and R itself (partially self-hosting). Precompiled
executable In computing, executable code, an executable file, or an executable program, sometimes simply referred to as an executable or binary, causes a computer "to perform indicated tasks according to encoded instruction (computer science), instructi ...
s are provided for various operating systems. R has a
command line interface A command-line interpreter or command-line processor uses a command-line interface (CLI) to receive commands from a user in the form of lines of text. This provides a means of setting parameters for the environment, invoking executables and pro ...
. Multiple third-party graphical user interfaces are also available, such as RStudio, an integrated development environment, and Jupyter, a notebook interface.


History

R is an open-source implementation of the
S programming language S is a statistical programming language developed primarily by John Chambers and (in earlier versions) Rick Becker and Allan Wilks of Bell Laboratories. The aim of the language, as expressed by John Chambers, is "to turn ideas into software, quic ...
combined with lexical scoping semantics from Scheme, which allow objects to be defined in predetermined blocks rather than the entirety of the code. S was created by Rick Becker, John Chambers, Doug Dunn, Jean McRae, and Judy Schilling at Bell Labs around 1976. Designed for statistical analysis, the language is an interpreted language whose code could be directly run without a compiler. Many programs written for S run unaltered in R. As a dialect of the
Lisp A lisp is a speech impairment in which a person misarticulates sibilants (, , , , , , , ). These misarticulations often result in unclear speech. Types * A frontal lisp occurs when the tongue is placed anterior to the target. Interdental lisping ...
language, Scheme was created by
Gerald J. Sussman Gerald Jay Sussman (born February 8, 1947) is the Panasonic Professor of Electrical Engineering at the Massachusetts Institute of Technology (MIT). He received his S.B. and Ph.D. degrees in mathematics from MIT in 1968 and 1973 respectively. ...
and Guy L. Steele Jr. at MIT around 1975. In 1991, statisticians Ross Ihaka and Robert Gentleman at the University of Auckland, New Zealand, embarked on an S implementation. It was named partly after the first names of the first two R authors and partly as a play on the name of S. They began publicizing it on the data archive StatLib and the ''s-news'' mailing list in August 1993. In 1995, statistician Martin Mächler convinced Ihaka and Gentleman to make R
free and open-source software Free and open-source software (FOSS) is a term used to refer to groups of software consisting of both free software and open-source software where anyone is freely licensed to use, copy, study, and change the software in any way, and the source ...
under the GNU General Public License. The first official release came in June 1995. The first official "stable beta" version (v1.0) was released on 29 February 2000. The
Comprehensive R Archive Network R packages are extensions to the R statistical programming language. R packages contain code, data, and documentation in a standardised collection format that can be installed by users of R, typically via a centralised software repository such a ...
(CRAN) was officially announced on 23 April 1997. CRAN stores R's executable files, source code, documentations, as well as packages contributed by users. CRAN originally had 3 mirrors and 12 contributed packages. As of January 2022, it has 101 mirrors and 18,728 contributed packages. In addition to hosting packages CRAN hosts binaries for major distributions of Linux, MacOS and Windows. The R Core Team was formed in 1997 to further develop the language. , it consists of Chambers, Gentleman, Ihaka, and Mächler, plus statisticians Douglas Bates, Peter Dalgaard,
Kurt Hornik Kurt is a male given name of Germanic or Turkish origin. ''Kurt'' or ''Curt'' originated as short forms of the Germanic Conrad, depending on geographical usage, with meanings including counselor or advisor. In Turkish, Kurt means "Wolf" and is ...
, Michael Lawrence, Friedrich Leisch, Uwe Ligges, Thomas Lumley, Sebastian Meyer, Paul Murrell, Martyn Plummer,
Brian Ripley Brian David Ripley FRSE (born 29 April 1952) is a British statistician. From 1990, he was professor of applied statistics at the University of Oxford and is also a professorial fellow at St Peter's College. He retired August 2014 due to ill he ...
, Deepayan Sarkar, Duncan Temple Lang,
Luke Tierney Luke Tierney is an American statistician and computer scientist. A fellow of the Institute of Mathematical Statistics since 1988 and of the American Statistical Association since 1991, Tierney is currently a professor of statistics at the Univers ...
, and Simon Urbanek, as well as computer scientist Tomas Kalibera. Stefano Iacus, Guido Masarotto, Heiner Schwarte, Seth Falcon, Martin Morgan, and Duncan Murdoch were members. In April 2003, the R Foundation was founded as a non-profit organization to provide further support for the R project.


Features


Data processing

R's
data structure In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, a ...
s include vectors, arrays, lists, and data frames. Vectors are ordered collections of values and can be mapped to arrays of one or more dimensions in a column major order. That is, given an ordered collection of dimensions, one fills in values along the first dimension first, then fill in one-dimensional arrays across the second dimension, and so on. R supports array arithmetics and in this regard is like languages such as APL and MATLAB. The special case of an array with two dimensions is called a
matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...
. Lists serve as collections of objects that do not necessarily have the same
data type In computer science and computer programming, a data type (or simply type) is a set of possible values and a set of allowed operations on it. A data type tells the compiler or interpreter how the programmer intends to use the data. Most progra ...
. Data frames contain a list of vectors of the same length, plus a unique set of row names. R has no scalar data type. Instead, a scalar is represented as a length-one vector. R and its libraries implement various statistical techniques, including linear, generalized linear and nonlinear modeling, classical
statistical tests A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...
,
spatial Spatial may refer to: *Dimension *Space *Three-dimensional space Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determ ...
and time-series analysis, classification, clustering, and others. For computationally intensive tasks, C, C++, and Fortran code can be linked and called at run time. Another of R's strengths is static
graphics Graphics () are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain. In contemporary usage, it includes a pictorial representation of data, as in design and manufacture ...
; it can produce publication-quality graphs that include mathematical symbols.


Programming

R is an interpreted language; users can access it through a command-line interpreter. If a user types 2+2 at the R command prompt and presses enter, the computer replies with 4. R supports procedural programming with functions and, for some functions, object-oriented programming with generic functions. Due to its S heritage, R has stronger object-oriented programming facilities than most statistical computing languages. Extending it is facilitated by its lexical scoping rules, which are derived from Scheme. R uses S-expressions to represent both data and code. R's extensible object system includes objects for (among others): regression models, time-series and geo-spatial coordinates. Advanced users can write C, C++, Java, .NET or Python code to manipulate R objects directly. Functions are first-class objects and can be manipulated in the same way as data objects, facilitating meta-programming that allows multiple dispatch. Function arguments are passed by value, and are lazy—that is to say, they are only evaluated when they are used, not when the function is called. A generic function acts differently depending on the classes of the arguments passed to it. In other words, the generic function dispatches the method implementation specific to that object's class. For example, R has a generic print function that can print almost every class of object in R with print(objectname). Many of R's standard functions are written in R, which makes it easy for users to follow the algorithmic choices made. R is highly extensible through the use of packages for specific functions and specific applications.


Packages

R's capabilities are extended through user-created ''packages'', which offer statistical techniques, graphical devices, import/export, reporting ( RMarkdown,
knitr knitr is an engine for dynamic report generation with R. It is a package in the programming language R that enables integration of R code into LaTeX, LyX, HTML, Markdown, AsciiDoc, and reStructuredText documents. The purpose of knitr is to allo ...
,
Sweave Sweave is a function in the statistical programming language R that enables integration of R code into LaTeX or LyX documents. The purpose is "to create dynamic reports, which can be updated automatically if data or analysis change". The data anal ...
), etc. These packages and their easy installation and use has been cited as driving the language's widespread adoption in
data science Data science is an interdisciplinary field that uses scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data, and apply knowledge from data across a br ...
. The packaging system is also used by researchers to organize research data, code and report files in a systematic way for sharing and archiving. Multiple packages are included with the basic installation. Additional packages are available on CRAN, Bioconductor, R-Forge, Omegahat, GitHub, and other repositories. The "Task Views" on the CRAN website lists packages in fields including Finance, Genetics, High Performance Computing, Machine Learning, Medical Imaging, Meta-Analysis, Social Sciences and Spatial Statistics. R has been identified by the FDA as suitable for interpreting data from clinical research. Microsoft maintains a daily snapshot of CRAN that dates back to Sept. 17, 2014. Other R package resources include R-Forge, a platform for the collaborative development of R packages. The Bioconductor project provides packages for genomic data analysis, including object-oriented data-handling and analysis tools for data from
Affymetrix Affymetrix is now Applied Biosystems, a brand of DNA microarray products sold by Thermo Fisher Scientific that originated with an American biotechnology research and development and manufacturing company of the same name. The Santa Clara, Califor ...
,
cDNA In genetics, complementary DNA (cDNA) is DNA synthesized from a single-stranded RNA (e.g., messenger RNA (mRNA) or microRNA (miRNA)) template in a reaction catalyzed by the enzyme reverse transcriptase. cDNA is often used to express a speci ...
microarray A microarray is a multiplex lab-on-a-chip. Its purpose is to simultaneously detect the expression of thousands of genes from a sample (e.g. from a tissue). It is a two-dimensional array on a solid substrate—usually a glass slide or silicon t ...
, and next-generation high-throughput sequencing methods. A group of packages called the Tidyverse, which can be considered a "dialect" of the R language, is increasingly popular among developers.Metacran
listed 7 of the 8 core packages of the Tidyverse in the list of most download R packages.
It strives to provide a cohesive collection of functions to deal with common data science tasks, including data import, cleaning, transformation and visualisation (notably with the ggplot2 package). Dynamic and interactive graphics are available through additional packages. R is one of 5 languages with an
Apache Spark Apache Spark is an open-source unified analytics engine for large-scale data processing. Spark provides an interface for programming clusters with implicit data parallelism and fault tolerance. Originally developed at the University of Californi ...
API, along with Scala, Java, Python, and SQL.


Milestones

A list of changes in R releases is maintained in various "news" files at CRAN.Changes in versions 3.0.0 onward: Earlier change logs (by major release number): * * * * * Some highlights are listed below for several major releases.


Interfaces

Various applications can be used to edit or run R code. Early developers preferred to run R via the command line console, succeeded by those who prefer an IDE. IDEs for R include (in alphabetical order
R.app
(OSX/macOS only), Rattle GUI, R Commander, RKWard, RStudio, and Tinn-R. R is also supported in multi-purpose IDEs such as
Eclipse An eclipse is an astronomical event that occurs when an astronomical object or spacecraft is temporarily obscured, by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three ce ...
via the StatET plugin, and Visual Studio via the R Tools for Visual Studio. Of these, RStudio is the most commonly used. Statistical frameworks which use R in the background include Jamovi and JASP. Editors that support R include
Emacs Emacs , originally named EMACS (an acronym for "Editor MACroS"), is a family of text editors that are characterized by their extensibility. The manual for the most widely used variant, GNU Emacs, describes it as "the extensible, customizable, s ...
,
Vim Vim means enthusiasm and vigor. It may also refer to: * Vim (cleaning product) * Vim Comedy Company, a movie studio * Vim Records * Vimentin, a protein * "Vim", a song by Machine Head on the album ''Through the Ashes of Empires'' * Vim (text ed ...
(Nvim-R plugin), Kate, LyX,
Notepad++ Notepad++ is a text and source code editor for use with Microsoft Windows. It supports tabbed editing, which allows working with multiple open files in a single window. The product's name comes from the C postfix increment operator. Notepad++ ...
, Visual Studio Code, WinEdt, and Tinn-R. Jupyter Notebook can also be configured to edit and run R code. R functionality is accessible from scripting languages including Python, Perl, Ruby, F#, and Julia. Interfaces to other, high-level programming languages, like Java and .NET C# are available.


Implementations

The main R implementation is written in R, C, and Fortran. Several other implementations aimed at improving speed or increasing extensibility. A closely related implementation is pqR (pretty quick R) by
Radford M. Neal Radford M. Neal is a professor at the Department of Statistics and Department of Computer Science at the University of Toronto, where he holds a research chair in statistics and machine learning. He studied computer science at the University of C ...
with improved memory management and support for automatic multithreading. Renjin and FastR are Java implementations of R for use in a
Java Virtual Machine A Java virtual machine (JVM) is a virtual machine that enables a computer to run Java programs as well as programs written in other languages that are also compiled to Java bytecode. The JVM is detailed by a specification that formally describes ...
. CXXR, rho, and Riposte are implementations of R in C++. Renjin, Riposte, and pqR attempt to improve performance by using multiple cores and deferred evaluation. Most of these alternative implementations are experimental and incomplete, with relatively few users, compared to the main implementation maintained by the R Development Core Team. TIBCO, who previous sold the commercial implementation S-PLUS, built a runtime engine called TERR, which is part of Spotfire. Microsoft R Open (MRO) is a fully compatible R distribution with modifications for multi-threaded computations. As of 30 June 2021, Microsoft started to phase out MRO in favor of the CRAN distribution.


Communities

R has local communities worldwide for users to network, share ideas, and learn. A growing number of R events bring users together, such as conferences (e.g. useR!, WhyR?, conectaR, SatRdays), meetups, as well as R-Ladies groups that promote gender diversity. The R Foundation taskforce focuses on women and other under-represented groups.


useR! conferences

The official annual gathering of R users is called "useR!". The first such event was useR! 2004 in May 2004, Vienna, Austria. After skipping 2005, the useR! conference has been held annually, usually alternating between locations in Europe and North America. History: * useR! 2006, Vienna, Austria * useR! 2007, Ames, Iowa, US * useR! 2008, Dortmund, Germany * useR! 2009, Rennes, France * useR! 2010, Gaithersburg, Maryland, US * useR! 2011, Coventry, United Kingdom * useR! 2012, Nashville, Tennessee, US * useR! 2013, Albacete, Spain * useR! 2014, Los Angeles, California, US * useR! 2015, Aalborg, Denmark * useR! 2016, Stanford, California, US * useR! 2017, Brussels, Belgium * useR! 2018, Brisbane, Australia * useR! 2019, Toulouse, France * useR! 2020, took place online due to COVID-19 pandemic * useR! 2021, took place online due to COVID-19 pandemic * useR! 2022, took place online due to COVID-19 pandemic The dates and the location for the next useR! event is to be decided as of end of 2022.


''The R Journal''

'' The R Journal'' is an
open access Open access (OA) is a set of principles and a range of practices through which research outputs are distributed online, free of access charges or other barriers. With open access strictly defined (according to the 2001 definition), or libre op ...
, refereed journal of the R project. It features short to medium length articles on the use and development of R, including packages, programming tips, CRAN news, and foundation news.


Comparison with alternatives

R is comparable to popular commercial statistical packages such as
SAS SAS or Sas may refer to: Arts, entertainment, and media * ''SAS'' (novel series), a French book series by Gérard de Villiers * ''Shimmer and Shine'', an American animated children's television series * Southern All Stars, a Japanese rock ba ...
, SPSS, and
Stata Stata (, , alternatively , occasionally stylized as STATA) is a general-purpose statistical software package developed by StataCorp for data manipulation, visualization, statistics, and automated reporting. It is used by researchers in many fie ...
. One difference is that R is available at no charge under a free software license. In January 2009, the '' New York Times'' ran an article charting the growth of R, the reasons for its popularity among data scientists and the threat it poses to commercial statistical packages such as SAS. In June 2017 data scientist Robert Muenchen published a more in-depth comparison between R and other software packages, "The Popularity of Data Science Software". R is more procedural than either SAS or SPSS, both of which make heavy use of pre-programmed procedures (called "procs") that are built-in to the language environment and customized by parameters of each call. R generally processes data in-memory, which limits its usefulness in processing larger files.


Commercial support

Although R is an
open-source Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use the source code, design documents, or content of the product. The open-source model is a decentralized sof ...
project, some companies provide commercial support and extensions. In 2007, Richard Schultz, Martin Schultz, Steve Weston and Kirk Mettler founded Revolution Analytics to provide commercial support for Revolution R, their distribution of R, which includes components developed by the company. Major additional components include: ParallelR, the R Productivity Environment IDE, RevoScaleR (for
big data Though used sometimes loosely partly because of a lack of formal definition, the interpretation that seems to best describe Big data is the one associated with large body of information that we could not comprehend when used only in smaller am ...
analysis), RevoDeployR, web services framework, and the ability for reading and writing data in the SAS file format.Morgan, Timothy Prickett (2011-02-07). "'Red Hat for stats' goes toe-to-toe with SAS". The Register, 7 February 2011. Retrieved from https://www.theregister.co.uk/2011/02/07/revolution_r_sas_challenge/. Revolution Analytics offers an R distribution designed to comply with established IQ/OQ/PQ criteria that enables clients in the pharmaceutical sector to validate their installation of REvolution R. In 2015, Microsoft Corporation acquired Revolution Analytics and integrated the R programming language into SQL Server, Power BI, Azure SQL Managed Instance, Azure Cortana Intelligence, Microsoft ML Server and Visual Studio 2017. In October 2011,
Oracle An oracle is a person or agency considered to provide wise and insightful counsel or prophetic predictions, most notably including precognition of the future, inspired by deities. As such, it is a form of divination. Description The word '' ...
announced the ''Big Data Appliance'', which integrates R,
Apache Hadoop Apache Hadoop () is a collection of open-source software utilities that facilitates using a network of many computers to solve problems involving massive amounts of data and computation. It provides a software framework for distributed storage ...
, Oracle Linux, and a
NoSQL A NoSQL (originally referring to "non- SQL" or "non-relational") database provides a mechanism for storage and retrieval of data that is modeled in means other than the tabular relations used in relational databases. Such databases have existed ...
database with Exadata hardware. ,
Oracle R Enterprise Oracle Database (commonly referred to as Oracle DBMS, Oracle Autonomous Database, or simply as Oracle) is a multi-model database management system produced and marketed by Oracle Corporation. It is a database commonly used for running online ...
Chris Kanaracus (2012)
''Oracle Stakes Claim in R With Advanced Analytics Launch''
PC World, February 8, 2012.
became one of two components of the "Oracle Advanced Analytics Option"Doug Henschen (2012)
''Oracle Stakes Claim in R With Advanced Analytics Launch''
InformationWeek, April 4, 2012.
(alongside Oracle Data Mining). IBM offers support for in- Hadoop execution of R, and provides a programming model for massively parallel in-database analytics in R. TIBCO offers a runtime-version R as a part of Spotfire. Mango Solutions offers a validation package for R, ValidR, to comply with drug approval agencies, such as the FDA. These agencies required the use of validated software, as attested by the vendor or sponsor.


Examples


Basic syntax

The following examples illustrate the basic syntax of the language and use of the command-line interface. (An expanded list of standard language features can be found in the R manual, "An Introduction to R".) In R, the generally preferred assignment operator is an arrow made from two characters <-, although = can be used in some cases. > x <- 1:6 # Create a numeric vector in the current environment > y <- x^2 # Create vector based on the values in x. > print(y) # Print the vector’s contents. 1 4 9 16 25 36 > z <- x + y # Create a new vector that is the sum of x and y > z # Return the contents of z to the current environment. 2 6 12 20 30 42 > z_matrix <- matrix(z, nrow=3) # Create a new matrix that turns the vector z into a 3x2 matrix object > z_matrix 1 2 , 2 20 , 6 30 , 12 42 > 2*t(z_matrix)-2 # Transpose the matrix, multiply every element by 2, subtract 2 from each element in the matrix, and return the results to the terminal. 1 2 3 , 2 10 22 , 38 58 82 > new_df <- data.frame(t(z_matrix), row.names=c('A','B')) # Create a new data.frame object that contains the data from a transposed z_matrix, with row names 'A' and 'B' > names(new_df) <- c('X','Y','Z') # Set the column names of new_df as X, Y, and Z. > print(new_df) # Print the current results. X Y Z A 2 6 12 B 20 30 42 > new_df$Z # Output the Z column 12 42 > new_df$Z

new_df Z'&& new_df /h1>

new_df$Z # The data.frame column Z can be accessed using $Z, Z' or syntax, and the values are the same. TRUE > attributes(new_df) # Print attributes information about the new_df object $names "X" "Y" "Z" $row.names "A" "B" $class "data.frame" > attributes(new_df)$row.names <- c('one','two') # Access and then change the row.names attribute; can also be done using rownames() > new_df X Y Z one 2 6 12 two 20 30 42


Structure of a function

One of R's strengths is the ease of creating new functions. Objects in the function body remain local to the function, and any data type may be returned. Example: # Declare function “f” with parameters “x”, “y“ # that returns a linear combination of x and y. f <- function(x, y) > f(1, 2) 11 > f(c(1,2,3), c(5,3,4)) 23 18 25 > f(1:3, 4) 19 22 25


Modeling and plotting

The R language has built-in support for data modeling and graphics. The following example shows how R can easily generate and plot a linear model with residuals. > x <- 1:6 # Create x and y values > y <- x^2 > model <- lm(y ~ x) # Linear regression model y = A + B * x. > summary(model) # Display an in-depth summary of the model. Call: lm(formula = y ~ x) Residuals: 1 2 3 4 5 6 7 8 9 10 3.3333 -0.6667 -2.6667 -2.6667 -0.6667 3.3333 Coefficients: Estimate Std. Error t value Pr(>, t, ) (Intercept) -9.3333 2.8441 -3.282 0.030453 * x 7.0000 0.7303 9.585 0.000662 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 3.055 on 4 degrees of freedom Multiple R-squared: 0.9583, Adjusted R-squared: 0.9478 F-statistic: 91.88 on 1 and 4 DF, p-value: 0.000662 > par(mfrow = c(2, 2)) # Create a 2 by 2 layout for figures. > plot(model) # Output diagnostic plots of the model.


Mandelbrot set

Short R code calculating Mandelbrot set through the first 20 iterations of equation ''z'' = ''z''2 + ''c'' plotted for different complex constants ''c''. This example demonstrates: * use of community-developed external libraries (called packages), in this case caTools package * handling of complex numbers * multidimensional arrays of numbers used as basic data type, see variables C, Z and X. install.packages("caTools") # install external package library(caTools) # external package providing write.gif function jet.colors <- colorRampPalette(c("green", "pink", "#007FFF", "cyan", "#7FFF7F", "white", "#FF7F00", "red", "#7F0000")) dx <- 1500 # define width dy <- 1400 # define height C <- complex(real = rep(seq(-2.2, 1.0, length.out = dx), each = dy), imag = rep(seq(-1.2, 1.2, length.out = dy), dx)) C <- matrix(C, dy, dx) # reshape as square matrix of complex numbers Z <- 0 # initialize Z to zero X <- array(0, c(dy, dx, 20)) # initialize output 3D array for (k in 1:20) write.gif(X, "Mandelbrot.gif", col = jet.colors, delay = 100)


See also

*
R package R packages are extensions to the R statistical programming language. R packages contain code, data, and documentation in a standardised collection format that can be installed by users of R, typically via a centralised software repository such as ...
* Comparison of numerical-analysis software * Comparison of statistical packages * List of numerical-analysis software * List of statistical software *
Rmetrics Rmetrics is a free, open-source and open development software project for teaching computational finance. Rmetrics is based primarily on the statistical R programming language, but does contain contributions in other programming languages, Fortr ...


Notes


References


External links

* of the R project
R Technical Papers
{{Portal bar, Computer programming Array programming languages Cross-platform free software Data mining and machine learning software Data-centric programming languages Dynamically typed programming languages Free plotting software Free statistical software Functional languages GNU Project software Literate programming Numerical analysis software for Linux Numerical analysis software for macOS Numerical analysis software for Windows Programming languages created in 1993 Science software Statistical programming languages Articles with example R code