Angry Birds is a video game franchise created by Finnish company Rovio Entertainment. The series focuses on multi-colored birds who try to save their eggs from green-colored pigs. Inspired by Crush the Castle, the game has been praised for its successful combination of fun gameplay, comical style, and low price. Its popularity led to many spin-offs, versions of Angry Birds being created for PCs and gaming consoles, a market for merchandise featuring its characters, a televised cartoon series, and a feature film. In January 2014 there had been over two billion downloads across all platforms, including both regular and special editions: as of July 2015, the series’ games have been downloaded more than three billion times collectively, making it the most downloaded freemium game series of all time. The original Angry Birds has been called "one of the most mainstream games out right now", "one of the great runaway hits of 2010", and "the largest mobile app success the world has seen so far". An animated feature film based on the series was released by Columbia Pictures on 20 May 2016, and the first main-series sequel, Angry Birds 2, was released on 30 July 2015. The first game in the series was initially released in December 2009 for Apple iOS. The company then released ports of the game for other touchscreen smartphone operating systems, including Android, Symbian, and Windows Phone, then video game consoles and PCs.

Bartholomew JoJo "Bart" Simpson is a fictional character in the American animated television series The Simpsons and part of the Simpson family. He is voiced by Nancy Cartwright and first appeared on television in The Tracey Ullman Show short "Good Night" on April 19, 1987. Cartoonist Matt Groening created and designed Bart while waiting in the lobby of James L. Brooks' office. Groening had been called to pitch a series of shorts based on his comic strip, Life in Hell, but instead decided to create a new set of characters. While the rest of the characters were named after Groening's family members, Bart's name is an anagram of the word brat. After appearing on The Tracey Ullman Show for three years, the Simpson family received its own series on Fox, which debuted December 17, 1989. At ten years old, Bart is the eldest child and only son of Homer and Marge, and the brother of Lisa and Maggie. Bart's most prominent and popular character traits are his mischievousness, rebelliousness and disrespect for authority. He has appeared in other media relating to The Simpsons – including video games, The Simpsons Movie, The Simpsons Ride, commercials, and comic books – and inspired an entire line of merchandise. In casting, Nancy Cartwright originally planned to audition for the role of Lisa, while Yeardley Smith tried out for Bart. Smith's voice was too high for a boy, so she was given the role of Lisa. Cartwright found that Lisa was not interesting at the time, so instead auditioned for Bart, which she thought was a better role. Hallmarks of the character include his chalkboard gags in the opening sequence; his prank calls to Moe; and his catchphrases "Eat my shorts", "¡Ay, caramba!", and "Don't have a cow, man!" Although, with the exception of "Ay, caramba!", they have been retired or not often used. During the first two seasons of The Simpsons, Bart was the show's breakout character and "Bartmania" ensued, spawning Bart Simpson-themed merchandise touting his rebellious attitude and pride at underachieving, which caused many parents and educators to cast him as a bad role model for children. Around the third season, the series started to focus more on the family as a whole, though Bart still remains a prominent character. Time named Bart one of the 100 most important people of the 20th century, and he was named "entertainer of the year" in 1990 by Entertainment Weekly. Nancy Cartwright has won several awards for voicing Bart, including a Primetime Emmy Award in 1992 and an Annie Award in 1995. In 2000, Bart, along with the rest of his family, was awarded a star on the Hollywood Walk of Fame. He has appeared in every Simpsons episode except Four Great Women and a Manicure.

Captain America is a fictional character appearing in American comic books published by Marvel Comics. Created by cartoonists Joe Simon and Jack Kirby, the character first appeared in Captain America Comics #1 (cover dated March 1941) from Timely Comics, a predecessor of Marvel Comics. Captain America was designed as a patriotic supersoldier who often fought the Axis powers of World War II and was Timely Comics' most popular character during the wartime period. The popularity of superheroes waned following the war and the Captain America comic book was discontinued in 1950, with a short-lived revival in 1953. Since Marvel Comics revived the character in 1964, Captain America has remained in publication. Captain America wears a costume that bears an American flag motif, and is armed with a nearly indestructible shield that he throws at foes. The character is usually depicted as the alter ego of Steve Rogers, a frail young man enhanced to the peak of human perfection by an experimental serum to aid the United States government's efforts in World War II. Near the end of the war, he was trapped in ice and survived in suspended animation until he was revived in the present day. Although Captain America often struggles to maintain his ideals as a man out of his time with its modern realities, he remains a highly respected figure in his community which includes becoming the long-time leader of the Avengers. Captain America was the first Marvel Comics character to have appeared in media outside comics with the release of the 1944 movie serial, Captain America. Since then, the character has been featured in other films and television series, more recently in the Marvel Cinematic Universe (MCU) portrayed by Chris Evans in Captain America: The First Avenger, The Avengers, Captain America: The Winter Soldier, Avengers: Age of Ultron, Captain America: Civil War, Spider-Man: Homecoming and the upcoming Avengers: Infinity War (2018) and its untitled sequel (2019). Captain America is ranked sixth on IGN's "Top 100 Comic Book Heroes of All Time" in 2011, second in their list of "The Top 50 Avengers" in 2012, and second in their "Top 25 best Marvel superheroes" list in 2014.

The Mandelbulb is a three-dimensional fractal, constructed by Daniel White and Paul Nylander using spherical coordinates in 2009. A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the 2-dimensional space of complex numbers. It is possible to construct Mandelbrot sets in 4 dimensions using quaternions and bicomplex numbers. White and Nylander's formula for the "nth power" of the vector v = ⟨ x , y , z ⟩ {\displaystyle {\mathbf {v} }=\langle x,y,z\rangle } in ℝ3 is v n := r n ⟨ sin ⁡ ( n θ ) cos ⁡ ( n ϕ ) , sin ⁡ ( n θ ) sin ⁡ ( n ϕ ) , cos ⁡ ( n θ ) ⟩ {\displaystyle {\mathbf {v} }^{n}:=r^{n}\langle \sin(n\theta )\cos(n\phi ),\sin(n\theta )\sin(n\phi ),\cos(n\theta )\rangle } where r = x 2 + y 2 + z 2 {\displaystyle r={\sqrt {x^{2}+y^{2}+z^{2}}}} , ϕ = arctan ⁡ ( y / x ) = arg ⁡ ( x + y i ) {\displaystyle \phi =\arctan(y/x)=\arg(x+yi)} , and θ = arctan ⁡ ( x 2 + y 2 / z ) = arccos ⁡ ( z / r ) {\displaystyle \theta =\arctan({\sqrt {x^{2}+y^{2}}}/z)=\arccos(z/r)} . The Mandelbulb is then defined as the set of those c {\displaystyle {\mathbf {c} }} in ℝ3 for which the orbit of ⟨ 0 , 0 , 0 ⟩ {\displaystyle \langle 0,0,0\rangle } under the iteration v ↦ v n + c {\displaystyle {\mathbf {v} }\mapsto {\mathbf {v} }^{n}+{\mathbf {c} }} is bounded. For n > 3, the result is a 3-dimensional bulb-like structure with fractal surface detail and a number of "lobes" depending on n. Many of their graphic renderings use n = 8. However, the equations can be simplified into rational polynomials when n is odd. For example, in the case n = 3, the third power can be simplified into the more elegant form: ⟨ x , y , z ⟩ 3 = ⟨ ( 3 z 2 − x 2 − y 2 ) x ( x 2 − 3 y 2 ) x 2 + y 2 , ( 3 z 2 − x 2 − y 2 ) y ( 3 x 2 − y 2 ) x 2 + y 2 , z ( z 2 − 3 x 2 − 3 y 2 ) ⟩ {\displaystyle \langle x,y,z\rangle ^{3}=\left\langle \ {\frac {(3z^{2}-x^{2}-y^{2})x(x^{2}-3y^{2})}{x^{2}+y^{2}}},{\frac {(3z^{2}-x^{2}-y^{2})y(3x^{2}-y^{2})}{x^{2}+y^{2}}},z(z^{2}-3x^{2}-3y^{2})\right\rangle } . The Mandelbulb given by the formula above is actually one in a family of fractals given by parameters (p,q) given by: v n := r n ⟨ sin ⁡ ( p θ ) cos ⁡ ( q ϕ ) , sin ⁡ ( p θ ) sin ⁡ ( q ϕ ) , cos ⁡ ( p θ ) ⟩ {\displaystyle {\mathbf {v} }^{n}:=r^{n}\langle \sin(p\theta )\cos(q\phi ),\sin(p\theta )\sin(q\phi ),\cos(p\theta )\rangle } Since p and q do not necessarily have to equal n for the identity |vn|=|v|n to hold. More general fractals can be found by setting v n := r n ⟨ sin ⁡ ( f ( θ , ϕ ) ) cos ⁡ ( g ( θ , ϕ ) ) , sin ⁡ ( f ( θ , ϕ ) ) sin ⁡ ( g ( θ , ϕ ) ) , cos ⁡ ( f ( θ , ϕ ) ) ⟩ {\displaystyle {\mathbf {v} }^{n}:=r^{n}\langle \sin(f(\theta ,\phi ))\cos(g(\theta ,\phi )),\sin(f(\theta ,\phi ))\sin(g(\theta ,\phi )),\cos(f(\theta ,\phi ))\rangle } for functions f and g.

Minions are the numerous creatures that appear in the Despicable Me franchise, which began with the eponymous 2010 film. They are also the official mascots of Illumination Entertainment, a division of Universal Studios, and have been described as being a corporate icon for Universal/Illumination's parent company Comcast on par with Disney's Mickey Mouse following Comcast's purchase of NBCUniversal. The Minions are small, yellow, melodious henchmen who wear overalls and goggles and have one or two eyes. They mostly speak incomprehensible gibberish, which is partly derived from other languages, including Bahasa Indonesia, French, English, Italian, Spanish, and Hindi. Although seemingly nonsensical, the English-sounding words are dubbed for every country, in order to make them recognizable. In Minions it is made clear that they have existed since the beginning of life on Earth, and desire above all else to serve the most terrible of villains. In the short film "Banana", the Minions are revealed to have an uncontrollable craving for fruits, especially bananas. They have most ordinary names, with Kevin, Stuart and Bob being the names of the lead trio in Minions, and Mel being the leader of the Minions in Despicable Me 3.

A nutcracker is a tool designed to open nuts by cracking their shells. There are many designs, including levers, screws, and ratchets. A well-known type portrays a person whose mouth forms the jaws of the nutcracker, though many of these are meant for decorative use.

Scooby-Doo is an American animated cartoon franchise, comprising many animated television series produced from 1969 to the present day. Writers Joe Ruby and Ken Spears created the original series, Scooby-Doo, Where Are You!, for Hanna-Barbera Productions in 1969. This Saturday-morning cartoon series featured four teenagers—Fred Jones, Daphne Blake, Velma Dinkley, and Norville "Shaggy" Rogers—and their talking brown Great Dane named Scooby-Doo, who solve mysteries involving supposedly supernatural creatures through a series of antics and missteps. Following the success of the original series, Hanna-Barbera and its successor Warner Bros. Animation have produced numerous follow-up and spin-off animated series and several related works, including television specials and made-for-TV movies, a line of direct-to-video films, and two Warner Bros.–produced theatrical feature films. Some versions of Scooby-Doo feature different variations on the show's supernatural theme, and include characters such as Scooby's cousin Scooby-Dum and nephew Scrappy-Doo in addition to or instead of some of the original characters. Scooby-Doo was originally broadcast on CBS from 1969 to 1975, when it moved to ABC. ABC aired the show until canceling it in 1986, and presented a spin-off featuring the characters as children, A Pup Named Scooby-Doo, from 1988 until 1991. New Scooby-Doo series aired as part of Kids' WB on The WB Network and its successor, The CW Network, from 2002 until 2008. Scooby-Doo! Mystery Incorporated aired on Cartoon Network from 2010 to 2013, and Be Cool, Scooby-Doo! debuted on Cartoon Network in 2015. Repeats of the various Scooby-Doo series are broadcast frequently on Cartoon Network and its sister channel Boomerang in the United States as well as other countries. In 2013, TV Guide ranked Scooby-Doo the fifth Greatest TV Cartoon of All Time.

Simulation is the imitation of the operation of a real-world process or system over time. The act of simulating something first requires that a model be developed; this model represents the key characteristics, behaviors and functions of the selected physical or abstract system or process. The model represents the system itself, whereas the simulation represents the operation of the system over time. Simulation is used in many contexts, such as simulation of technology for performance optimization, safety engineering, testing, training, education, and video games. Often, computer experiments are used to study simulation models. Simulation is also used with scientific modelling of natural systems or human systems to gain insight into their functioning, as in economics. Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Simulation is also used when the real system cannot be engaged, because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed but not yet built, or it may simply not exist. Key issues in simulation include acquisition of valid source information about the relevant selection of key characteristics and behaviours, the use of simplifying approximations and assumptions within the simulation, and fidelity and validity of the simulation outcomes. Procedures and protocols for model verification and validation are an ongoing field of academic study, refinement, research and development in simulations technology or practice, particularly in the field of computer simulation.

Skeletal animation is a technique in computer animation in which a character (or other articulated object) is represented in two parts: a surface representation used to draw the character (called skin or mesh) and a hierarchical set of interconnected bones (called the skeleton or rig) used to animate (pose and keyframe) the mesh. While this technique is often used to animate humans or more generally for organic modeling, it only serves to make the animation process more intuitive and the same technique can be used to control the deformation of any object — a door, a spoon, a building, or a galaxy. When the animated object is more general than, for example, a humanoid character the set of bones may not be hierarchical or interconnected, but it just represents a higher level description of the motion of the part of mesh or skin it is influencing. The technique was introduced in 1988 by Nadia Magnenat Thalmann, Richard Laperrière, and Daniel Thalmann. This technique is used in virtually all animation systems where simplified user interfaces allows animators to control often complex algorithms and a huge amount of geometry; most notably through inverse kinematics and other "goal-oriented" techniques. In principle, however, the intention of the technique is never to imitate real anatomy or physical processes, but only to control the deformation of the mesh data.

solidThinking is a software company developing Evolve, a 3D modeling and rendering software and Inspire, a concept generation tool.