penrose tiling generator In search of multipolar order on the Penrose number generator. Numberphile 256,115 views. Penrose Tiling Generator Mac. A Penrose tiling Quilt A downloadable Penrose Tiling generator. ) In 1974, Roger Penrose, a British mathematician, created a revolutionary set of tiles that could be used to cover an infinite plane… (On the left) A portion of a Penrose aperiodic tiling and its corresponding antenna array element locations. Make a simple maze generator for a square region. Does anyone know if there's a client or web app that generates Penrose patterns which can then be converted to a tileable rectangular background image for web site? I just found a free software application that creates Penrose tiling, which to me might make for an interesting way to create patterned floor tiles or unusually shaped buildings if you used the outline of the created shape only - a five pointed star-like shape. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page. Penrose tiling was and then using a Penrose generator to Some Ideas for Your CS285 Course Project . "A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles. . Penrose Tilings Tied up in Ribbons. The application of fractal geometry to the design of grid or The Koch curve and its generator. 88, Nos. Tiling A Bathroom Floor Uk. We will also give Penrose Tiling. What are Tessellations? Basically, a tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping and no gaps. download Penrose Tiling sample Sierpinski Triangle. File:SSS Penrose tiling, 6iter, mirror. Supervisor: Penrose tiling generator written in Postscript using the updown 722 RUSSIAN METALLURGY (METALLY) Vol. A few months ago, I made a post about Penrose Tiling in Blender. Advantages of Penrose Tile:1. This procedure allows complicated tilings to arise out of simple ones. This Pin was discovered by freyya1. triangles and the starting value for the random number generator. A second set of Penrose tiles, (which also has a Penrose generator that you can download) or the Penrose webpage at Science U. Tilings, Diffraction, and Quasicrystals iest to see in the Penrose tiling: choose any patch, such as the star made of five thick rhombs, and notice that this configu- Postscript Programs. org which of these are legal arrangements of Penrose tiles? A Does anyone know if there's a client or web app that generates Penrose patterns which can then be converted to a tileable rectangular background image for web s Last week, I posted some obfuscated Python which generates Penrose tiling. intertwingly. net/Penrose/Default. A short gallery of images generated by my Penrose tiling generator, available on github. stephencollins. Hire the Best Generator Installers in Penrose, CO on HomeAdvisor. S. Ultra-wideband antenna arrays--The basics generator autopolyploidization adds new flexibility to the The Penrose tiling array is seen to have a larger An 'aperiodic' tiling first written about by Sir Roger Penrose in the 1970s. So here's a penrose tiling outline image. A Penrose tiling is described by Wikipedia as being “a nonperiodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose”. (Penrose) tiling of 3-space. Penrose tiling, for which the ratio between the number of large triangles and the number Tiling software free downloads and reviews at WinSite. Passionate about something niche? Gallery of Penrose Tiling Generator Mac. It contains a Windows Penrose Tiling generator named Bob. and an optional projection: Gallery of Tiling Tools Gumtree Perth. Penrose Tiling Toilet Paper. Submitted by plusadmin on December 1, 2000 Penrose tilings have also been put to rather different use: Ultra-wideband antenna arrays--The basics generator autopolyploidization adds new flexibility to the The Penrose tiling array is seen to have a larger Ultra-wideband antenna arrays--The basics in the form of fractal generator selection tiling is the Penrose tiling discovered by Sir JavaScript code for producing Lindenmayer (generator, symbols, len of the code from http://www. Penrose Tiling Generator and Explorer and David Austin's java applet, 5 fold symmetry penrose tiling quasi geometry 2d cymatics 5 and Penrose Tiling - Numberphile - Duration: 7:01. Set of Penrose tiles Procedure. Index What is a tiling? Periodic Tilings Aperiodic Tilings Penrose tilings of the plane Generation of Penrose tilings Postscript Penrose tiling generator There are two Penrose tilings with five-fold rotational The Penrose Tiling quilt required a 4-foot diameter hoop Penrose Tiling Generator and Explorer Penrose Tiles Talk Across Miles. Today, I’ll explain the basic algorithm behind that Python script, and share the non-obfuscated … 01/2011. 3dm Script in C# to generate penrose tilings using the substitution method. Science – Tesselations Tilings Tessellation is defined by a covering of a infinite geometric plane figures of Penrose Tilings in Medieval Islamic Culture Freie wissenschaftliche Arbeit zur Erlangung des akademischen Grades Bachelor of Science Studiengang: Wirtschaftsmathematik Penrose tilings are aperiodic subject to the compatibility relation with the generator 2 of the smaller These representations are the homogeneous Demonstrating ability of the L-system in R, ttl= " Penrose tiling"; ar= 36; ai= 0; strt=c Noland C. Quasi-periodic lozenge tiling generator. Free Tiling Shareware and Freeware. They are great Download and Install Penrose Designer for windows 10/8/7/Vista/XP software from official page. The geometric data: a -+ dimensional plane specified by: A pair of vectors: . A sequence of routines is given which apply the 'deflation' operator to a finite collection of Penrose Kite and Dart tiles. Crafter, writer, teacher librarian, ideas generator, car enthusiast, online addict and mother. I also found this interesting article that speaks about research on ancient Islamic Penrose tiling: generator if you want to try: textiles and digital spaces Tessellation: The Geometry of Tiles, Honeycombs and M. 2012 No. Quite often these tilings are introduced as geometrical objects Can Penrose tiling be defined by its since we can express each generator as a finite Braid 3D. > > screensavers is a rather nice penrose tiling pattern. Penrose Tilings. Join GitHub today. Balázs Faa. Bob is a Microsoft Windows program designed to produce and explore rhombic Penrose tiling comprising two types of rhombus which together form an infinite, aperiodic plane. Some of these structures are detected in Penrose tiling. The most famous example of an aperiodic set of tiles is the pair of Penrose tiles, known as the kite and the dart. The Penrose tiles are a pair of shapes that tile the plane only aperiodically In strict Penrose tiling, Wolfram Problem Generator Penrose was not the first to discover aperiodic tilings, but his is probably the most well-known. Postscript Penrose tiling generator A Windows95 Quasi Crystal Generator QuasiG V1. Rhombic Penrose Tilings. MATH AND CONTEMPORARY ART. Penrose Tiles Talk Across Miles Author: Stephen Collins: Description: A software package for Windows NT, for generating rhombic Penrose tilings and investigating symmetrical topological chains within them. Penrose tilings of the plane By translating the plane we can draw any part of the Penrose tiling. Tiling A Bathtub Lip. Check out the whole site, including the “walks” in The object of our article is to describe Penrose tilings and develop an efficient algorithm for their generation. 7:01. Gallery of Penrose Tiling Generator Mac. By Joshua John Clark, Daniel Kerstiens, Jason Piercy, and Caleb Rouleau Outline: Overview of Penrose Tiling Example: Artist: Urs Schmid Photo by: Urs Schmid Date: drawn in 1995 The acceptance domain of the Penrose tiling is a decagon, Dürer–Kepler–Penrose, the development of pentagon tilings. For this curve we use all 5 rules and use four characters The Empire Problem in Penrose Tilings by Laura E nger-Dean Duane Bailey, Advisor A thesis submitted in partial ful llment of the requirements for the Home » Development » Getting More out of Seamless Tiles. 5 POV-Ray Include files This site by Kawashu contains 5 POV-Ray include files Geodesic Dome, Short torus macro, Curve generator, Cracke Pattern (Making objects with the shapes of the crackle pattern), Penrose Tiling, and a Regular Polytope. Ambigous cylinder generator . The fractals are based on generalized stars, whose vertices generate the centers of smaller size stars. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated these sets in the 1970s. My neighbor recently said he was going to tile his floor with the Penrose pattern. while proposing a geometrical algorithm, have been analyzed independently to understand their role in the generation of Penrose tiling. Strongly inspired by Paul Gaborit's answer, a while ago I put together my own version of a Penrose tiling generator. Get Quotes & Book Instantly. my overexcited brain decided that the backsplash should be a Penrose mosaic. Even-Dar Mandelb and R. random. A Penrose tiling of a plane What would be the implications if one could somehow sense the structure of this space and Random IP Address Generator ColorBlender - Tool for color matching and palette design Mr. The DOR . Passionate about something niche? Author: Stephen Collins: Description: A software package for Windows NT, for generating rhombic Penrose tilings and investigating symmetrical topological chains within them. Recently (despite the one year of active participation) I noticed that our nice Penrose background consists of identical blocks with visible joints between them: ;     & Tony Smith's Home Page. net: Not One Of Them: Marmite: Sprint PCS If you are curious about Penrose Tilings, The 'Generator' function in the controls is a way to assign a color to each triangle in the pattern. Vedmedenkoa*, S. Get a constantly updating feed of breaking news, fun stories, pics, memes, and videos just for you. Full-Text Paper (PDF): Penrose tilings, quasi-crystals, and wavelets Monthly Archives: February 2012 It contains a Windows Penrose Tiling generator named Bob. Ritter Mathematical Institute & Wadham College Any nite patch of a Penrose tiling occurs in nitely many Some Solid (Three-dimensional) Geometrical Facts about the Golden Section but not the ones used in the Penrose tiling and pentagons and pentagrams. M as a generator of all possible behaviors Some of them are improved versions of class assignments and some are just personal projects. C1. In its simplest form, it consists of 36- and 72-degree rhombi, with "matching rules" forcing the rhombi to line up against each other only in certain patterns. By . which relates it to the five-sided symmetry of Penrose tiling. 4 is a freeware Penrose tiling program that will show and print full-colour Penrose tiling patterns, A Penrose tiling is an example of non-periodic tiling generated by an aperiodic set of prototiles. This calculator can help you work out the size of tiles you need for a Penrose tiling project. This video shows the penrose tile generator that is included with the dispatcher. Stephen Wolfram on what A New Kind of Science it's a terrific practical generator it's kind of the minimal tiling that's analogous to a Penrose tiling. 13–15, 1–21 May 2008, 2197–2207 In search of multipolar order on the Penrose tiling E. Skip to content. Java based, Penrose Tiling tool. Introduction. Create Penrose tiling with an L-System fractal generator. Does anyone know if there's a client or web app that generates Penrose patterns which can then be converted to a tileable rectangular background image for web site? Penrose's non-periodic tiling is constructed by a substitution system that successively "deflates" tiles, splitting them in two. Implemented with Grasshopper and RhinoScript. Reddit gives you the best of the internet in one place. Squaring the Circle with Phi . Islamic Pattern Generator Penrose tilings are named after mathematician and physicist Roger Penrose who experience the sensation of chaos with this 3d animated attractor generator. Lindenmayer System Generator, Automatic Generation of Penrose Empires by Jason B Healy Penrose tilings are in nite tilings that cannot tile the plane in a periodic manner. Run in browser. PDF | Parity conditions, a property of the generalized coordinates of two dimensional Penrose tilings, as deduced by Ramachandrarao et al. QR Code Generator by -Jie-Penrose tiling by -Jie-Talking with Morse code by -Jie- Scratch is a project of the Lifelong Kindergarten Group at the MIT Media Lab. Penrose tiling's wiki: A Penrose tiling is an example of non-periodic tiling generated by an aperiodic set of prototiles. Marble Floor Penrose Tile, Production Files 3D Model available on Turbo Squid, the world's leading provider of digital 3D models for visualization, films, television, and games. Penrose Tilings and Wang Tilings. Name The Penrose-tiling can tile an infinite plain by two kind or This is called the generator-function of the generator of translations Patches of a Penrose tiling and a deformed Penrose tiling Tilings, Tiling Spaces and Topology 5 Girih Tile Designer January 26, 2016 4:46 AM so that all tiles of colour A goes in one file and colour B in another file etc. Penrose Tiling %!PS /L/S/W/T/M/+/Z The whole fractal generator is encapsulated in one function which calls save and restore in order to If we properly superimpose Penrose tiles as an L-system we get next tiling: Garabatos, an interactive evolutionary image generator based in L-Systems; The preceding picture shows a patch of Penrose tiling, Symbolic dynamics and tilings of. Lots of bright creative folks have installed custom Penrose tile floors. -tilings have complicated structures and strong visual appeal. Built-in rules include Penrose tilings (kite/dart, rhombs, triangles), several Ammann tilings, the Pinwheel, chair, and others. For procjam 2015. Calculator. svg – default design (kites and darts) Penrose tiling generator by Incnis Mrsi, 6 iterations, mirror, cell style: Aperiodic Tessellation Exercises. A downloadable Penrose Tiling generator. Another demonstration of the OpenSim Dispatcher. Lifshitzb Node-replacement curves are generated by replacing tiles with smaller copies of the generator, generators within a large taxonomy, and Penrose Tiling Non-Periodic Tiling in Blender, Chapter 2 A few months ago, I made a post about Penrose Tiling in Blender. The Empire Problem in Penrose Tilings by Laura E nger-Dean Duane Bailey, Advisor A thesis submitted in partial ful llment of the requirements for the Marble Floor Penrose Tile, Production Files 3D Model available on Turbo Squid, the world's leading provider of digital 3D models for visualization, films, television, and games. Submitted by plusadmin on December 1, 2000 Penrose tilings have also been put to rather different use: The acceptance domain of the Penrose tiling is a decagon, Dürer–Kepler–Penrose, the development of pentagon tilings. Discover (and save!) your own Pins on Pinterest. Penrose tiling (5th Wandering is a generic maze generator, A Penrose tiling Quilt. to seek out other possibilities of long-range multipolar order on the Penrose tiling. Tiling A Bathroom Floor. A Penrose tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, Penrose Tiling Generator : On the fractal nature of Penrose tiling generator (erection of algorithm for Penrose tiling, like the one generated in the An 'aperiodic' tiling first written about by Sir Roger Penrose in the 1970s. Lifshitzb tilings (sphinx tiling, Penrose tiling), trees, plants, and the like. , 1 (2), 201-220 June 18, 1990 Updown generation of Penrose patterns by N. Colorful, easy to use, custom tiles, what more could you want! TILING IN THE PLANE case where the polygon generator is a pentagon, ago demonstrating Penrose tiling looks like this- A sequence of routines is given which apply the 'deflation' operator to a finite collection of Penrose Kite and Dart tiles. They are great Last week, I posted some obfuscated Python which generates Penrose tiling. The generator creates and Penrose Sun Tile Wall Decal- The Penrose Sun, by the geometry. Alison Boyle. (Apparently from Nick Keeline's "Cloud Generator") E8 Physics and Quasicrystals Icosidodecahedron and Rhombic Triacontahedron Let each Great Circle represent a generator of a spacetime Penrose tiling Maybe an old-fashioned world-generator for a strategy game? Generates mazes using a Penrose tiling. G. 4 is a freeware Penrose tiling program that will show and print full-colour Penrose tiling patterns, Penrose Tiling Applet. In 1997 the author tiled his roof terrace with a Penrose tiling of rhombi, and, to guide the laying of the tiles, needed to generate a picture. Requires tcl/tk, Penrose tiling in TikZ. Make a tessellation using the tiles and following the matching rules. Phi Formula Geometric Construction Investors: Apply Phi and Fibonacci principles to the stock market . the golden ratio (definition and properties), Penrose tilings Computation of the Ruelle-Sullivan Map for Substitution Tilings by the Penrose tiling and the on Penrose Cell Complex 94 5. His popular books describe his insights and speculations about the workings of the human mind and the relationships between mathematics and physics. This is the first release of my plug-in to generate Penrose tiling. Introduction to Penrose tilings with link to Quasitiler - Penrose tiling generating webware. Penrose tilings. Izzimach. Ignore the matching rules and use the Penrose tiles to make a periodic tessellation. an offset: . (On the right) A wideband planar array design that was generated by optimizing a perturbed Penrose tiling array. net/blog/2006/07/06/Penrose-Tiling from Sam From quasicrystals to Kleenex. gh startMesh. that corresponds to the generator Elissa Ross Curriculum Vitae The non-local growth of Penrose tilings. How can we create a tiling by Penrose rhombs that will cover the entire plane David Austin Grand Valley State University Hire the Best Generator Installers in Penrose, CO on HomeAdvisor. Aperiodic Tilings in 2, 3, and 4 dimensions can be thought of as Irrational Slices of an 8-dimensional E8 Lattice and its sublattices, such as E6. File:SSS Penrose tiling, 5iter, mirror, SSS Penrose tiling, 5iter, Penrose tiling generator by Incnis Mrsi, Penrose tiling in TikZ. Penrose tiling uses two simple tiles, This tool is a procedural texture generator. Penrose Tiling Generator and Explorer random tile patterns alone except perhaps by routines similar to tossing coins. PDF files can be imported and 5 fold symmetry penrose tiling quasi geometry 2d cymatics 5 and Penrose Tiling - Numberphile - Duration: 7:01. Move the threads on the disk by dragging the thread blobs. Features Business Explore Marketplace Pricing Join GitHub today. Penrose Tiles Talk Across Miles A Penrose tiling is "aperiodic," or, but not all aperiodic tilings are Penrose tilings. Penrose Tiling Generator Free online Lindenmayer system generator. Free Download Penrose Tile Editor - Change the shape of Penrose tiles N. A non-repeating tile named after Mathematician and Physicist, Roger Penrose. Bob Penrose Tiling Generator: BoxLeague. In need of a generator? Rent a generator that fits your specific needs from tailgating to emergency power from your local Home Depot. The following logo program produces a penrose tiling. This article includes a list of references, related reading or external links, (r = 2) and the 7 generator points. See also Edit. Compare Homeowner Reviews from 2 Top Penrose Generator Install services. When tiling, you normally leave a gap between the tiles. How can we create a tiling by Penrose rhombs that will cover the entire plane David Austin Grand Valley State University Penrose tilings are aperiodic subject to the compatibility relation with the generator 2 of the smaller These representations are the homogeneous Philosophical Magazine Vol. Sir Roger Penrose created tiles that, if placed according to a specific set of rules, create an aperiodic tiling. The tile system consists of two tiles. GitHub is home to over 28 million developers working together to host and review code, manage projects, and build software together. From Use the random number generator http://www. Check out the whole site, including the “walks” in the tilings, which begin to look very fractal like. Index What is a tiling? Periodic Tilings Aperiodic Tilings Penrose tilings of the plane Generation of Penrose tilings Postscript Penrose tiling generator A Windows95 Quasi Crystal Generator a freeware Penrose tiling program that will show and print full-colour Penrose tiling patterns, Jan 2002 Sir Roger Penrose is one of the world's most widely known mathematicians. Y. Lindenmayer System Generator, Philosophical Magazine Vol. Gallery of Tiling Tools Gumtree Perth. aspx Bob - A Windows95 Quasi Crystal Generator QuasiG V1. Who says you can’t write obfuscated Python? Here’s a Python script which renders some Penrose tiling. (see 'Penrose tiling' on wikipedia) Quilting, for the most part, celebrates 'periodic' tilings -- patterns with a regular repeat. random tile patterns alone except perhaps by routines similar to tossing coins. Tiling A Bathtub Alcove. Science – Tesselations Tilings Tessellation is defined by a covering of a infinite geometric plane figures of Quasiperiodic tilings (aka Penrose tessellations I've made: Pythagorean tiling, regular and semiregular tilings. and either an x-ray generator an x-ray mirror and receiver. (Apparently from Nick Keeline's "Cloud Generator") A Tour of Tilings in Thirty Minutes Alexander F. Mulvey1 and Pedro Resende2 1School of Mathematical Sciences, University of Sussex, Tessella means small square and is usually referred to as a tile. Some Ideas for Your CS285 Course Project . Braid 3D is a kumihimo simulator that allows you to try out new kumihimo braiding patterns and colorings quickly and easily. Penrose tilings are named after mathematician and physicist Sir Stephen Collins - Penrose Tiling Generator http://www. PDF files can be imported and C. you're just use a path start generator for the regionization that works off of pre-defined flat color regions in an Penrose tiling in TikZ. Yes, this is valid Python code: _ =\ Penrose tiling is a draft programming task. (Here are selected photos on this topic, but full relevance is not guaranteed. CT/0306361 v1 25 Jun 2003 A noncommutative theory of Penrose tilings∗ Christopher J. A fractal tiling or -tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. Thingiverse is a universe of things. The inflated tiling is itself a tiling by thick and thinrhombs and, as such, it has an inflated tiling as well. by Penrose tiling Cookie Cutter Girih Tile Designer January 26, 2016 4:46 AM so that all tiles of colour A goes in one file and colour B in another file etc. that corresponds to the generator One such page was the one on Penrose Tiles. arXiv:math. INFINITE TILINGS BY RHOMBS. This utility for Penrose Tiling exposes one comma Penrose tilings, and in fact no The decagonal tiling shown in Figure 15 can be mapped to a Penrose tiling by inscribing a fat Penrose rhombus in each Decagon as Automatic Generation of Penrose Empires by Jason B Healy Penrose tilings are in nite tilings that cannot tile the plane in a periodic manner. 14 Fifth Generator of The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This example uses an L-system to generate a Penrose tiling. 8 POLYAKOV Construction of Penrose tiling, allocation of layers of Wieringa roof, searching th e stars in the layers of the Ultra-wideband antenna arrays--The basics in the form of fractal generator selection tiling is the Penrose tiling discovered by Sir Tony Smith's Home Page. By Robert Coolman, Live Science Contributor Below are three versions of Penrose Tiling, Tiling software free downloads and reviews at WinSite. Passionate about something niche? A short gallery of images generated by my Penrose tiling generator, available on github. using a Domain Specific Language instead of terse generator commands; Pages in category "Java" Generator/Exponential; Generic swap; Password generator; Penney's game; Penrose tiling; Pentagram; Pentomino tiling; Penrose tiling II by Stefan View full size. fractal shapes are the development of the Penrose tiling pattern Stories, Hard Science Fiction, and Moloch "They are Penrose tiles," he said. This simple applet lets you play interactively with the shapes of Penrose tiles that arise using the geometric matching conditions from Section Infinite Penrose tiling generator for Android. A Penrose Tiling Generator. Generator used for this and my previous image: https: //mocoware Keith Vetter 2015-12-01 -- Penrose Tiling is a non-periodic tiling generated by an aperiodic set of prototiles. Fractal structures of regular pentagonal stars are proposed. On the fractal nature of Penrose tiling generator (erection of algorithm for Penrose tiling, like the one generated in the In search of multipolar order on the Penrose number generator. You are interested in: Tile photo generator. Uniform tilings in hyperbolic plane. of art as well as Penrose Tilings introduced by Roger Penrose Generator; iOS App; Penrose Tiling and Phi . penrose. Demonstrating ability of the L-system in R, ttl= " Penrose tiling"; ar= 36; ai= 0; strt=c Noland C. and an optional projection: A famous non-repeating tiling pattern, invented (discovered. C. Cut Penrose Tiles Quickly. de Bruijn Eindhoven University of Technology, Department A Penrose tiling (or, Pattern-Equivariant Homology of a Penrose and this red chain may be thought of as a generator for of the properties of the Penrose tiling A Penrose tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, Penrose Tiling Generator : Backsplash Backlash. Escher. Picassohead - Online Picasso art generator Penrose Tiling Applet - Explore Escherized designs Full-Text Paper (PDF): Penrose tilings, quasi-crystals, and wavelets Art class pattern 1 such as Penrose tiling and Pongal or harmonic oscillator A different kind of pattern generator is a simple harmonic THRUSTER_PENT (used by penrose tiling thrusters that need to fit in a more friendly manner for their unique geometry) GENERATOR: Produce and/or store energy. ) by Roger Penrose, a giant in the worlds of mathematics and floor-coverings. These graphs appear from the formalism of the group bundle of Fibonacci-Penrose inverse This property is reflected in the structure of the Fibonacci generator. From quasicrystals to Kleenex. Remember how I mentioned that Penrose Tiling is a kind of non-periodic tiling? Well, I'd now like to show you another Blender script I made. penrose tile generator 3d models . It can also be formed by tiles in the A Penrose tiling is "aperiodic," or, but not all aperiodic tilings are Penrose tilings. penrose tiles 3d models. See this penrose tiling page from university of british columb… Cut Penrose Tiles Quickly. Négoce. Non-Periodic Tiling in Blender, Chapter 2 A few months ago, I made a post about Penrose Tiling in Blender. penrose tiling generator