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Plotting algorithms for the Mandelbrot set
There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software. These programs use a variety of algorithms to determine the color of individual pixels efficiently. == Escape time algorithm == The simplest algorithm for generating a representation of the Mandelbrot set is known as the "escape time" algorithm. A repeating calculation is performed for each x, y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel. === Unoptimized naïve escape time algorithm === In both the unoptimized and optimized escape time algorithms, the x and y locations of each point are used as starting values in a repeating, or iterating calculation (described in detail below). The result of each iteration is used as the starting values for the next. The values are checked during each iteration to see whether they have reached a critical "escape" condition, or "bailout". If that condition is reached, the calculation is stopped, the pixel is drawn, and the next x, y point is examined. For some starting values, escape occurs quickly, after only a small number of iterations. For starting values very close to but not in the set, it may take hundreds or thousands of iterations to escape. For values within the Mandelbrot set, escape will never occur. The programmer or user must choose how many iterations–or how much "depth"–they wish to examine. The higher the maximal number of iterations, the more detail and subtlety emerge in the final image, but the longer time it will take to calculate the fractal image. Escape conditions can be simple or complex. Because no complex number with a real or imaginary part greater than 2 can be part of the set, a common bailout is to escape when either coefficient exceeds 2. A more computationally complex method that detects escapes sooner, is to compute distance from the origin using the Pythagorean theorem, i.e., to determine the absolute value, or modulus, of the complex number. If this value exceeds 2, or equivalently, when the sum of the squares of the real and imaginary parts exceed 4, the point has reached escape. More computationally intensive rendering variations include the Buddhabrot method, which finds escaping points and plots their iterated coordinates. The color of each point represents how quickly the values reached the escape point. Often black is used to show values that fail to escape before the iteration limit, and gradually brighter colors are used for points that escape. This gives a visual representation of how many cycles were required before reaching the escape condition. To render such an image, the region of the complex plane we are considering is subdivided into a certain number of pixels. To color any such pixel, let c {\displaystyle c} be the midpoint of that pixel. We now iterate the critical point 0 under P c {\displaystyle P_{c}} , checking at each step whether the orbit point has modulus larger than 2. When this is the case, we know that c {\displaystyle c} does not belong to the Mandelbrot set, and we color our pixel according to the number of iterations used to find out. Otherwise, we keep iterating up to a fixed number of steps, after which we decide that our parameter is "probably" in the Mandelbrot set, or at least very close to it, and color the pixel black. In pseudocode, this algorithm would look as follows. The algorithm does not use complex numbers and manually simulates complex-number operations using two real numbers, for those who do not have a complex data type. The program may be simplified if the programming language includes complex-data-type operations. for each pixel (Px, Py) on the screen do x0 := scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2.00, 0.47)) y0 := scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1.12, 1.12)) x := 0.0 y := 0.0 iteration := 0 max_iteration := 1000 while (xx + yy ≤ 22 AND iteration < max_iteration) do xtemp := xx - yy + x0 y := 2xy + y0 x := xtemp iteration := iteration + 1 color := palette[iteration] plot(Px, Py, color) Here, relating the pseudocode to c {\displaystyle c} , z {\displaystyle z} and P c {\displaystyle P_{c}} : z = x + i y {\displaystyle z=x+iy\ } z 2 = x 2 + 2 i x y {\displaystyle z^{2}=x^{2}+2ixy} - y 2 {\displaystyle y^{2}\ } c = x 0 + i y 0 {\displaystyle c=x_{0}+iy_{0}\ } and so, as can be seen in the pseudocode in the computation of x and y: x = R e ( z 2 + c ) = x 2 − y 2 + x 0 {\displaystyle x=\mathop {\mathrm {Re} } (z^{2}+c)=x^{2}-y^{2}+x_{0}} and y = I m ( z 2 + c ) = 2 x y + y 0 . {\displaystyle y=\mathop {\mathrm {Im} } (z^{2}+c)=2xy+y_{0}.\ } To get colorful images of the set, the assignment of a color to each value of the number of executed iterations can be made using one of a variety of functions (linear, exponential, etc.). One practical way, without slowing down calculations, is to use the number of executed iterations as an entry to a palette initialized at startup. If the color table has, for instance, 500 entries, then the color selection is n mod 500, where n is the number of iterations. === Optimized escape time algorithms === The code in the previous section uses an unoptimized inner while loop for clarity. In the unoptimized version, one must perform five multiplications per iteration. To reduce the number of multiplications the following code for the inner while loop may be used instead: x2:= 0 y2:= 0 w:= 0 while (x2 + y2 ≤ 4 and iteration < max_iteration) do x:= x2 - y2 + x0 y:= w - x2 - y2 + y0 x2:= x x y2:= y y w:= (x + y) (x + y) iteration:= iteration + 1 The above code works via some algebraic simplification of the complex multiplication: ( i y + x ) 2 = − y 2 + 2 i y x + x 2 = x 2 − y 2 + 2 i y x {\displaystyle {\begin{aligned}(iy+x)^{2}&=-y^{2}+2iyx+x^{2}\\&=x^{2}-y^{2}+2iyx\end{aligned}}} Using the above identity, the number of multiplications can be reduced to three instead of five. The above inner while loop can be further optimized by expanding w to w = x 2 + 2 x y + y 2 {\displaystyle w=x^{2}+2xy+y^{2}} Substituting w into y = w − x 2 − y 2 + y 0 {\displaystyle y=w-x^{2}-y^{2}+y_{0}} yields y = 2 x y + y 0 {\displaystyle y=2xy+y_{0}} and hence calculating w is no longer needed. The further optimized pseudocode for the above is: x:= 0 y:= 0 x2:= 0 y2:= 0 while (x2 + y2 ≤ 4 and iteration < max_iteration) do x2:= x x y2:= y y y:= 2 x y + y0 x:= x2 - y2 + x0 iteration:= iteration + 1 Note that in the above pseudocode, 2 x y {\displaystyle 2xy} seems to increase the number of multiplications by 1, but since 2 is the multiplier the code can be optimized via ( x + x ) y {\displaystyle (x+x)y} . == Coloring algorithms == In addition to plotting the set, a variety of algorithms have been developed to efficiently color the set in an aesthetically pleasing way show structures of the data (scientific visualisation) === Histogram coloring === A more complex coloring method involves using a histogram which pairs each pixel with said pixel's maximum iteration count before escape/bailout. This method will equally distribute colors to the same overall area, and, importantly, is independent of the maximum number of iterations chosen. This algorithm has four passes. The first pass involves calculating the iteration counts associated with each pixel (but without any pixels being plotted). These are stored in an array IterationCounts[x][y], where x and y are the x and y coordinates of said pixel on the screen respectively. The first step of the second pass is to create an array NumIterationsPerPixel[n], where the array size n is the maximum iteration count. Next, one must iterate over the array of pixel-iteration count pairs IterationCounts[x][y], and retrieve each pixel's saved iteration count, i, via e.g. i = IterationCounts[x][y]. After each pixel's iteration count i is retrieved, it is necessary to index the NumIterationsPerPixel array at i and increment the indexed value (which is initially zero) -- e.g. NumIterationsPerPixel[i] = NumIterationsPerPixel[i] + 1. for (x = 0; x < width; x++) do for (y = 0; y < height; y++) do i:= IterationCounts[x][y] NumIterationsPerPixel[i]++ The third pass iterates through the NumIterationsPerPixel array and adds up all the stored values, saving them in total. The array index represents the number of pixels that reached that iteration count before bailout. total: = 0 for (i = 0; i < max_iterations; i++) do total += NumIterationsPerPixel[i] After this, the fourth pass begins and all the values in the IterationCounts array are indexed, and, for each iteration count i, associated with each pixel, the count is added to a global sum of all the iteration counts from 1 to i in the NumIterationsPerPixel array . This value is then normalized by dividing the sum by the total value computed earlier. hue[][]:= 0.0 for (x = 0; x < width; x++) do for (y = 0; y < height; y++) do iteration:= Iteration
Tom's Planner
Tom's Planner is a web-based tool and application service provider for project planning, management and collaboration. == History == Tom's Planner is based on Curaçao. In November 2009, it announced its public beta launch on TechCrunch and moved out of beta in August 2010. In 2013 Tom's Planner acquired its competitor Gantto. == Software == Tom's Planner is project management software that enables the creation of project schedules (Gantt charts) using a visual perspective. Tom's Planner uses the Freemium Business Model. Users can register for a free account or choose a paid version. Tom's Planner is available in five languages and is used by thousands of users on a daily basis in more than 100 countries worldwide. Customers range from fortune 500 companies to small mom-and-pop shops. == Reviews == Tom's Planner has been reviewed by PC World, TechCrunch, Lifehacker, and several other periodicals.
NationBuilder
NationBuilder is a Los Angeles-based technology start-up that develops content management and customer relationship management (CRM) software. Although the company initially targeted political campaigns and nonprofit organizations, it later expanded its marketing efforts to include other people and organizations trying to build an online following, such as artists, musicians and restaurants. The software uses voter data such as names, addresses and other information, such as previous voting records in the case of political campaigns, to allow users to centralize, build and manage campaigns by integrating various communication tools like websites, newsletters, text messaging and social media channels under one platform. Among other features, the software enables users to quickly create websites, build databases through registrations, send targeted newsletters, analyse data from multiple sources and leverage micro-donations. The software's appeal towards political campaigns comes from the combination of a number of previously separate campaigning services, channels and data sources into a single platform that was presented as a facile solution for non-technical users and which enabled political campaigners to quickly deploy campaigns by convincing numerous people to donate. == History == NationBuilder was founded in 2009 in Los Angeles by Jim Gilliam and launched in 2011. In 2012 Joe Green joined NationBuilder as co-founder and president. He left that role 11 months later in February 2013. Gilliam was previously a movie-maker who co-founded Brave New Films with Robert Greenwald and had sought funding for his films through crowd-sourcing. Green, who studied organizing at Harvard and was Mark Zuckerberg's roommate, is also the co-founder of the Causes Facebook app; he left NationBuilder in 2013. Since its founding, the company has helped campaigns raise $1.2 billion. In 2012, NationBuilder announced that 1,000 subscribers have used its software to amass 2.5 million supporters and raise $12 million in campaign donations. In 2015 it has helped raise $264 million, recruit over one million volunteers and coordinate some 129,000 events. By 2016, the company said its software was used by about 40 percent of all contested elections at the state and national level in the U.S., which included 3,000 political campaigns. Using such software is easier in the U.S. than Europe, where comprehensive data protection and privacy laws are in effect since 2018. The Scottish National Party was the first political party to use NationBuilder, harvesting vast amounts of data pertaining to voter activity via websites such as Facebook and Twitter. This revelation prompted outrage over privacy concerns. Guy Herbert of the No2ID campaign called the use of such data harvesting tools by the SNP "utterly hypocritical". == Funding == Investors in NationBuilder include Chris Hughes - the Facebook co-founder, Sean Parker - first president of Facebook and co-founder of Napster and Causes, Dan Senor - the former Republican foreign-policy adviser and Ben Horowitz, co-founder of Andreessen Horowitz. In 2012, it has raised $6.3 million in funding from a number of investors. == Notable implementations == The software is reported to have played a role in some public elections in Europe, the US and New Zealand, as well as non-profit initiatives, and political parties in Australia. Notable users include Bernie Sanders, Mitch McConnell, Andrew Yang, Theresa May, Amnesty International, the NAACP and Donald Trump. === France === La République En Marche used NationBuilder in their campaign for the 2017 National Assembly. === New Zealand === NationBuilder's services are used by New Zealand political parties, including in the campaigns of both the National and Labour parties in the 2017 general election. === United Kingdom === Despite stricter data protection and privacy laws in the UK and EU, NationBuilder was used to significant impact in a number of UK elections, most notably in the 2016 campaign for withdrawal of the United Kingdom from the European Union. The company later made a public announcement that both sides in that campaign had used its software. === United States === NationBuilder was used in the Donald Trump presidential campaign to advance his election efforts and eventually win the 2016 presidential race. Jill Stein of the Green Party, Republican Rick Santorum, and independent supporters of various candidates all used NationBuilder during their 2016 runs for president. During the 2018 US election cycle, political entities paid more than $1 million for the use of NationBuilder. Among the entities paying the most were Donald J. Trump for President, Prosperity Action and the Republican Party of Tennessee.
Color space
A color space is a specific organization of colors. In combination with color profiling supported by various physical devices, it supports reproducible representations of color – whether such representation entails an analog or a digital representation. A color space may be arbitrary, i.e. with physically realized colors assigned to a set of physical color swatches with corresponding assigned color names (including discrete numbers in – for example – the Pantone collection), or structured with mathematical rigor (as with the NCS System, Adobe RGB and sRGB). A "color space" is a useful conceptual tool for understanding the color capabilities of a particular device or digital file. When trying to reproduce color on another device, color spaces can show whether shadow/highlight detail and color saturation can be retained, and by how much either will be compromised. A "color model" is an abstract mathematical model describing the way colors can be represented as tuples of numbers (e.g. triples in RGB or quadruples in CMYK); however, a color model with no associated mapping function to an absolute color space is a more or less arbitrary color system with no connection to any globally understood system of color interpretation. Adding a specific mapping function between a color model and a reference color space establishes within the reference color space a definite "footprint", known as a gamut, and for a given color model, this defines a color space. For example, Adobe RGB and sRGB are two different absolute color spaces, both based on the RGB color model. When defining a color space, the usual reference standard is the CIELAB or CIEXYZ color spaces, which were specifically designed to encompass all colors the average human can see. Since "color space" identifies a particular combination of the color model and the mapping function, the word is often used informally to identify a color model. However, even though identifying a color space automatically identifies the associated color model, this usage is incorrect in a strict sense. For example, although several specific color spaces are based on the RGB color model, there is no such thing as the singular RGB color space. == History == In 1802, Thomas Young postulated the existence of three types of photoreceptors (now known as cone cells) in the eye, each of which was sensitive to a particular range of visible light. Hermann von Helmholtz developed the Young–Helmholtz theory further in 1850: that the three types of cone photoreceptors could be classified as short-preferring (blue), middle-preferring (green), and long-preferring (red), according to their response to the wavelengths of light striking the retina. The relative strengths of the signals detected by the three types of cones are interpreted by the brain as a visible color. But it is not clear that they thought of colors as being points in color space. The color-space concept was likely due to Hermann Grassmann, who developed it in two stages. First, he developed the idea of vector space, which allowed the algebraic representation of geometric concepts in n-dimensional space. Fearnley-Sander (1979) describes Grassmann's foundation of linear algebra as follows: The definition of a linear space (vector space)... became widely known around 1920, when Hermann Weyl and others published formal definitions. In fact, such a definition had been given thirty years previously by Peano, who was thoroughly acquainted with Grassmann's mathematical work. Grassmann did not put down a formal definition—the language was not available—but there is no doubt that he had the concept. With this conceptual background, in 1853, Grassmann published a theory of how colors mix; it and its three color laws are still taught, as Grassmann's law. As noted first by Grassmann... the light set has the structure of a cone in the infinite-dimensional linear space. As a result, a quotient set (with respect to metamerism) of the light cone inherits the conical structure, which allows color to be represented as a convex cone in the 3- D linear space, which is referred to as the color cone. == Examples == Colors can be created in printing with color spaces based on the CMYK color model, using the subtractive primary colors of pigment (cyan, magenta, yellow, and key [black]). To create a three-dimensional representation of a given color space, we can assign the amount of magenta color to the representation's X axis, the amount of cyan to its Y axis, and the amount of yellow to its Z axis. The resulting 3-D space provides a unique position for every possible color that can be created by combining those three pigments. Colors can be created on computer monitors with color spaces based on the RGB color model, using the additive primary colors (red, green, and blue). A three-dimensional representation would assign each of the three colors to the X, Y, and Z axes. Colors generated on a given monitor will be limited by the reproduction medium, such as the phosphor (in a CRT monitor) or filters and backlight (LCD monitor). Another way of creating colors on a monitor is with an HSL or HSV color model, based on hue, saturation, brightness (value/lightness). With such a model, the variables are assigned to cylindrical coordinates. Many color spaces can be represented as three-dimensional values in this manner, but some have more, or fewer dimensions, and some, such as Pantone, cannot be represented in this way at all. == Conversion == Color space conversion is the translation of the representation of a color from one basis to another. This typically occurs in the context of converting an image that is represented in one color space to another color space, the goal being to make the translated image look as similar as possible to the original. == RGB density == The RGB color model is implemented in different ways, depending on the capabilities of the system used. The most common incarnation in general use as of 2021 is the 24-bit implementation, with 8 bits, or 256 discrete levels of color per channel. Any color space based on such a 24-bit RGB model is thus limited to a range of 256×256×256 ≈ 16.7 million colors. Some implementations use 16 bits per component for 48 bits total, resulting in the same gamut with a larger number of distinct colors. This is especially important when working with wide-gamut color spaces (where most of the more common colors are located relatively close together), or when a large number of digital filtering algorithms are used consecutively. The same principle applies for any color space based on the same color model, but implemented at different bit depths. == Lists == CIE 1931 XYZ color space was one of the first attempts to produce a color space based on measurements of human color perception (earlier efforts were by James Clerk Maxwell, König & Dieterici, and Abney at Imperial College) and it is the basis for almost all other color spaces. The CIERGB color space is a linearly-related companion of CIE XYZ. Additional derivatives of CIE XYZ include the CIELUV, CIEUVW, and CIELAB. === Generic === RGB uses additive color mixing, because it describes what kind of light needs to be emitted to produce a given color. RGB stores individual values for red, green and blue. RGBA is RGB with an additional channel, alpha, to indicate transparency. Common color spaces based on the RGB model include sRGB, Adobe RGB, ProPhoto RGB, scRGB, and CIE RGB. CMYK uses subtractive color mixing used in the printing process, because it describes what kind of inks need to be applied so the light reflected from the substrate and through the inks produces a given color. One starts with a white substrate (canvas, page, etc.), and uses ink to subtract color from white to create an image. CMYK stores ink values for cyan, magenta, yellow and black. There are many CMYK color spaces for different sets of inks, substrates, and press characteristics (which change the dot gain or transfer function for each ink and thus change the appearance). YIQ was formerly used in NTSC (North America, Japan and elsewhere) television broadcasts for historical reasons. This system stores a luma value roughly analogous to (and sometimes incorrectly identified as) luminance, along with two chroma values as approximate representations of the relative amounts of blue and red in the color. It is similar to the YUV scheme used in most video capture systems and in PAL (Australia, Europe, except France, which uses SECAM) television, except that the YIQ color space is rotated 33° with respect to the YUV color space and the color axes are swapped. The YDbDr scheme used by SECAM television is rotated in another way. YPbPr is a scaled version of YUV. It is most commonly seen in its digital form, YCbCr, used widely in video and image compression schemes such as MPEG and JPEG. xvYCC is an international digital video color space standard published by the IEC (IEC 61966-2-4). It is based on the ITU BT.601 and BT.709
Butler in a Box
Butler in a Box was an early voice-controlled home automation device developed in 1983 by magician Gus Searcy and programmer Franz Kavan. The device allowed users to control various home electronics, such as lights and phones, using voice commands. It predated modern smart speakers and virtual assistants by several decades. == History == The idea for the Butler in a Box originated in 1983 when Searcy was asked by friends why he couldn't simply command lights to turn on and off if he could pull rabbits out of hats, given his background as a professional magician. Searcy partnered with former IBM programmer Kavan to develop the device, with their first prototype being named "Sidney". The Butler in a Box combined remote control technology with voice recognition to enable control of home devices. However, it faced challenges due to the technological limitations of the era and its high price point of nearly $1,500 (equivalent to around $3,700 in 2021). == Features and functionality == Users could activate the Butler in a Box by speaking a wake word, typically a traditional butler name, and the device would address the user as "boss". It was capable of performing tasks such as: Turning lights on and off, controlling individual zones if lights were connected to remote control modules Making and receiving phone calls Setting timers Pairing with sensors to function as a security alarm system However, the device required extensive voice training for each user, a time-consuming process compared to modern voice recognition. Additionally, settings and trained commands would be lost if power was out for over 3 hours due to the volatile memory technology used at the time. == Reception and legacy == While innovative for its time, the Butler in a Box did not achieve widespread commercial success due to its high price and the technical limitations of the 1980s. Nevertheless, it served as an important early step in the development of home automation and showcased the potential for voice-controlled technology to enhance accessibility and convenience in the home. Decades later, products like Amazon Alexa, Google Home, and Apple's Siri would make voice-controlled smart home devices commonplace and affordable, building on the groundwork laid by early attempts like the Butler in a Box.
Stripe, Inc.
Stripe, Inc. is an Irish and American multinational financial services and software as a service (SaaS) company dual-headquartered in South San Francisco, California, United States, and Dublin, Ireland. The company primarily offers payment-processing software and application programming interfaces for e-commerce websites and mobile applications. Stripe is the largest privately owned financial technology company with a valuation of about $159 billion and over $1.9 trillion in payment volume processed in 2025, processing transactions for 5 million businesses in that year. == History == Irish entrepreneur brothers John and Patrick Collison founded Stripe in Palo Alto, California, in 2010, and serve as the company's president and CEO, respectively. In 2011 the company received a $2 million investment, including contributions from Elon Musk, PayPal founder Peter Thiel, Irish entrepreneur Liam Casey, and venture capital firms Sequoia Capital, Andreessen Horowitz, and SV Angel. In March 2013, Stripe made its first acquisition, Kickoff, a chat and task-management application. In 2012 the company moved from Palo Alto to San Francisco. In October 2019, the company announced that it would be moving from the South of Market area to Oyster Point in the neighbouring city of South San Francisco in 2021. In February 2021, Mark Carney, former governor of the Bank of Canada and of the Bank of England, was appointed to the company's board. Carney stepped down from his role with the company in 2025 in order to run for the leadership of the Liberal Party. Stripe acquired accountancy platform Recko in October 2021 whose solution was to be added to Stripe's existing suite of financial tools. In January 2022, Stripe entered a five-year partnership with Ford Motor Company. Through the deal, Stripe would handle transactions for consumer vehicle orders and reservations. That same month, Stripe partnered with Spotify to help the company monetize subscriptions. In April 2022, Twitter announced that it would partner with Stripe, Inc. (digital payments processor) for piloting cryptocurrency pay-outs for limited users in the platform. In April 2022, Stripe announced its strategic partnership with UK-based financial technology company ION. The Wall Street Journal reported in July 2022 that the company's internal share price had fallen, causing its implied valuation to drop from $95 billion to $74 billion. In November 2022, the company announced it intended to initiate layoffs, terminating some 14% of its workforce. Throughout 2022 and 2023, the company announced a number of large enterprise customers, including Airbnb, Amazon, Microsoft, Uber, BMW, Maersk, Zara, Lotus, Alaska Airlines, Le Monde, and Toyota. The company also announced in March 2023 that OpenAI is working with Stripe to commercialize its generative AI technology. In January 2025, Stripe sent layoff notices to nearly 300 workers, primarily affecting roles in Product, Operations and Engineering. The company experienced controversy when the company sent a cartoon picture of a duck to the laid-off employees. Stripe's Chief People Officer Rob McIntosh later apologized for the mistake. After re-enabling cryptocurrency pay-ins in April 2024, starting with USDC, Stripe completed the acquisition of Bridge in February 2025. The acquisition of the two-year-old stablecoin platform company is valued at $1.1 billion. In June 2025, the company acquired Privy, which powers crypto wallets. In September 2025, Stripe announced it was powering Instant Checkout in ChatGPT and released Agentic Commerce Protocol for agentic commerce, which was co-developed with OpenAI. In October 2025, the company opened its second headquarters in Dublin, Ireland. In February 2026, Stripe was valued at $159 billion in a tender offer posted for employees and shareholders. The tender offer was about a 70% increase from Stripe's previous valuation published in February 2025, where it was valued at $91.5 billion. Stripe also announced that its total volume increased to $1.9 trillion USD in 2025, a 34% increase from 2024. == Technology company == === Payment processing === Stripe provides application programming interfaces that web developers can use to integrate payment processing into their websites and mobile applications. The company introduced Stripe Connect in 2012, a multiparty payments solution that lets software developers embed payments natively into their products. In April 2018, Stripe released antifraud tools, branded "Radar", that block fraudulent transactions. The same year, it expanded its services to include a billing product for online businesses, allowing businesses to manage subscription recurring revenue and invoicing. Stripe's point-of-sale service called Terminal was made available to US users on 11 June 2019. Terminal had previously been invitation-only. Terminal is currently available in Australia, Canada, France, Germany, Ireland, the Netherlands, New Zealand, Singapore, and the United Kingdom. The service offers physical credit-card readers designed to work with Stripe. On 5 September 2019, Stripe launched a merchant cash-advance scheme called Stripe Capital. The scheme allows Stripe merchants to request an advance on future payments they expect to process through their Stripe merchant account. In June 2021, the company launched Stripe Tax, a service to allow businesses to automatically calculate and collect sales tax, VAT, and GST, initially rolling out to 30 countries and all US states. As of 2025, it has been made available in 102 countries. In May that year, Stripe introduced Payment Links, a no-code product allowing businesses to create a link to a checkout page and begin accepting payments on social platforms or direct channels. In January 2022, Stripe agreed to acquire Terminal manufacturing partner BBPOS, allowing the company to bring the hardware development of Terminal readers in-house. In February, it was announced as Apple's first partner on in-person Tap to Pay, which enables businesses to accept contactless payments using an iPhone and a partner-enabled iOS app. In May, Stripe announced Data Pipeline, a tool for Stripe users who store data with Amazon Redshift or Snowflake Data Cloud. Data Pipeline syncs Stripe data and reports with Amazon Redshift or Snowflake Data Cloud, where they can be queried in combination with other business information. That month, the company also introduced Stripe Financial Connections, enabling businesses to establish direct connections with their customers’ bank accounts to verify accounts for payments and pay-outs, check balances to reduce payment failures, and cut fraud by confirming bank account ownership. In September 2023, Stripe announced that its optimized checkout suite allowed businesses to offer their customers more than 100 payment methods. In May 2025, Stripe announced a new AI foundational model for payments, and introduced stablecoin powered accounts. === Corporate finance === In July 2018, Stripe introduced Stripe Issuing, a product that allows online businesses and platforms to create their own physical and digital credit and debit cards. === Atlas === On 14 February 2016, the company launched the Atlas platform to help start-ups register as US corporations, targeting foreign entrepreneurs. The platform was originally invitation-only. In March 2016, Cuba was added to the list of countries covered under the program. Originally, companies registered using Atlas were set up as Delaware-based C corporations. As of 30 April 2018, the option to be registered as limited liability companies was added. Companies set up using Atlas automatically had a business bank account and Stripe merchant account set up. === Link === In May 2021, Stripe launched Link, a service for saving and auto-filling payment details when paying via Stripe. The service supported payments in over 185 countries and Stripe reported plans to make it available to platform businesses through its API. In September 2025, Patrick Collison announced that Link had surpassed 200 million users. === Other === In 2018, Stripe started a publishing company named Stripe Press to promote ideas that support businesses. In 2019, Stripe began offering loans and credit cards to businesses in the United States. The company stated that loans are approved automatically using machine-learning models, with no human intervention. The following year, the company introduced Stripe Treasury, which provides its platform users APIs to embed financial services, allowing their customers to send, receive, and store funds. In October 2020, Stripe announced Stripe Climate, a service for businesses to fund atmospheric carbon research and capture. In 2022, Stripe started a new subsidiary called Frontier that would direct spending on carbon removal. It announced $925 million in funding from major Silicon Valley companies to fund start up companies performing carbon capture to kick-start the industry. Stripe Identity, launched in Ju