The Matrix

Welcome, to the desert of the real

The Matrix : William Gibson is known to be the originator of the word "cyberspace", and he is the genuine creator of the Matrix, in his first novel Neuromancer (1984); and the followings, included within the Sprawl trilogy, Count Zero (1986) and Mona Lisa Overdrive (1988):

A year here and he still dreamed of cyberspace, hope fading nightly. All the speed he took, all the turns he'd taken and the corners he'd cut in Night City, and still he'd see the matrix in his sleep, bright lattices of logic unfolding across that colorless void....

Authoring as well the short story Johnny Mnemonic (1981) -whose film was also featured by Keanu Reeves in 1995-, and scripts for The X-Files, Gibson outlined the characters of Neo (Bobby Newmark in Count Zero) and Trinity (Molly, in Johnny Mnemonic and Neuromancer), and aroused such ideas like direct downloading precise instructions into their minds on how to fly an helicopter or mastering Kung-fu.

The Matrix plays with the concept of Technological Singularity, expression that was spreaded by the mathematician Vernor Vinge to describe the turning point in which social and technological development are due to:

- creation of a computer that surpasses human capacity,
- neural network aware of own consciousness,
- interaction between man and machine that allows to develop its skills,
- or through biological manipulation of human beings

The Matrix also have similarities to Akira (Katsuhiro Otomo, 1988) and GITS (Ghost in the Shell, by Masanori Ota, under pseudonym Masamune Shirow, hit the screen in 1995), what was actually admited by the Wachowski Bros in The Animatrix. Indeed there are several "borrowed" scenes and story lines. Likewise Dark City (Alex Proyas, 1998) has too many resemblances to The Matrix (even used same sets), as well as The Thirteenth Floor (Josef Rusnak, 1999), that was also premiered before. Both are great movies, despite they have not gotten the same acknowledgment as The Matrix did.

But if there do exists a source from where obvious parallelisms with The Matrix come up, are the comic series The Invisibles, from Grant Morrison: the look of Morpheus and the character King Mob; the famous jump of Neo's training with Morpheus, or Dane Jack Frost and Tom O'Bedlan in the comic; or the interrogation scene between Agent Smith and Morpheus, or Sir Miles and King Mob in The Invisibles, to mention a few. There are even some back references, from Morrison to The Matrix, in retaliation, like the "born" (or awakening) scene of Neo, after deciding to fall into the rabbit hole. In fact, King Mob (Morpheus) bears great resemblance to Morrison.

When Morpheus depicts Matrix to Neo, he sentences "Welcome, to the desert of the real". This same sentence misreads the one in sociologist Jean Baudrillard's book Simulacra and Simulation, concerned about how technology influences social relations, hyperreality denying reality.

Outstanding visual effects, specially John Gaeta's "Bullet Time" technique (even its real owner is Michel Gondry, in a Rolling Stones video), The Matrix has been the film that branded the new science-fiction aesthetics.

Soccer ball

(with Alias|wavefront PowerAnimator, but fits Maya or Rhino easily)

Theoretical basics : A (classical) soccer ball is made up of 20 hexagons and 12 pentagons, distributed so that 5 hexagons surround each pentagon, and each hexagon is surrounded by 3 pentagons alternated with 3 hexagons. A surface like this cannot be geometrically flat, it will always be curve.

Both pentagons and hexagons have sides of equal length, and this distance is the same of its radius (from any vertex to its center). Given the side length L, we can obtain the radius of curvature R of the soccer ball.

To deduce the radius R of the sphere we use the relation between it and the perimeter P of its equator 2 · pi · R = P, where the pi number is approximately 3.141592. Due to the layout of hexagons over the ball surface, you can see that the perimeter is equal to 15 times the length L. Therefore, if the circle has 360 degrees, then each side L of the polygon corresponds to 360º / 15 = 24º of circumference.

If we take as 1 unit (any) the flat length L' of the polygons' sides (hexagon and pentagon), then the length of its side on the curved surface of the ball (L) will be higher.

Using the expression for trigonometric sine of an angle, we can calculate the radius R of the ball sin(24º) = L' / R, so R = L' / sin(24º) = 1 / 0.4067366430758 = 2.458593335574 units. We can also infer the length L of an arc of circumference, using the same expression as for the perimeter P, since P is proportional to 2 · pi · (360 degrees), L = 2 · pi · (24 º / 360 º) · R = 1.029852953906 units.

Modeling : Let's build the soccer ball upon intersections with a sphere, whose sections and radii of curvature are different, depending on hexagons or pentagons. These caps are generated from revolution curves.

1. First the hexagon, in the Front view, create a circle of radius 1 and 6 sections from a primitive (Objects folder), and place it in the origin (coordinates) with the grid magnet (Alt key). From the Right view, now draw a spline with CVs (Control Vertex): the first point with a magnet on the upper Edit Point of the circle (Ctrl key); the second point is placed with a shift, in relative coordinates, to the position r0 .05 0; the third point of the curve at 0 .05 -.1; the fourth at 0 .1 -.3; the fifth at 0 .1 -.4; and the sixth and last in absolute coordinates at position a0 .3 0. Once we have the spline, we place its pivot in the origin (XForm folder; Pivot icon) with command a0 0 0. Revolution now the curve over the Y axis and generate a surface of 12 sections (Surface folder; Revolve icon). Then template the generating curve and the circle (ObjectDisplay menu; Toggle Template option or Alt+T keys). Now move the generated surface (removing its Construction History) to the relative position r0 2.158593335574, which is the ball radius R minus the height of the sphere cap 0.3. In this position, move the pivot again, now from the surface to the origin: a0 0 0; because when we rotate the cap, we will do it on the center of the ball (the origin of coordinates).

To get the positions of the hexagons that form the soccer ball, we calculate the offset angles with respect to the original position.

Positions of the hexagons near the equator of the ball have their center shifted by an angle, in the X coordinate, proportional to half the apothem a of the hexagon. If the apothem a of the hexagon is, by Pythagoras theorem, a^2 = L'^2 - (L'/2)^2, then a = .8660254037844 units. The angle proportional to the apothem a, with respect to the 24º angle that corresponds to the hexagon's side length L', is a · 24° / L' = 20.78460969083º. Therefore, half the apothem a represents half of this angle: 10.39230484541º.

Rotate (XForm folder; Rotate icon) the surface of the first hexagon, in relative, and over the X coordinate, a r10.39230484541 angle. Duplicate the sphere cap of the first hexagon (Edit menu; Duplicate Object option), and rotate in relative coordinates the copy around the X axis by an equivalent angle to twice (2) the apothem a of the hexagon 41.56921938165.

The position of the third hexagon is shifted (rotated) over the first, and the Z axis, an angle equal to 3/4 the distance between the hexagon's vertexes; that is 1.5 · L = 1.5 · 24° = 36°. And over the X axis an angle corresponding to the apothem a. Let's duplicate then the first surface, and rotate the third copy in relative -20.78460969083 0 36.

The fourth hexagon, duplicate this time the third cap, and rotate this fourth surface -41.56921938165 over the X axis.

The remaining surfaces, we obtain them duplicating (Edit menu; Duplicate Object option) the four we already built, with a rotation over the Z axis by 72º, and a number of 4 duplications. This will generate the rest of sphere caps corresponding to hexagons, and thus closing the soccer ball surface.

2. The process to build the surfaces of pentagons is similar, but must take into account that the initial reference circle radius will be smaller than that of the hexagon. The side L' must be the same for the two polygons. Therefore, the radius r is calculated using sin(36º) = (L'/2) / r, where 36° matches half the angle of the arc that corresponds to a one side of the pentagon (360º / 5 = 72º). Thus, the radius r = (L'/2) / sin(36º) = 0.5 / 0.5877852522925 = 0.850650808352 units.

The pentagon, in the Front view, first create a circle of 5 sections from a primitive, and place it in the origin with the grid magnet. From the Right view, now draw a spline with CVs: the first point with a magnet on the upper Edit Point of the circle; place the second point shifted, in relative coordinates, to the position r0 .1 0; the third point of the curve at 0 .05 -.1; the fourth at 0 .05 -.3; the fifth at 0 .1 -.3; and the sixth and last in absolute coordinates at position a0 .3 0. Once we have the spline, we place its pivot in the origin with command a0 0 0. Revolution now the curve over the Y axis and generate a surface of 10 sections. Then template the generating curve and the circle. Now move the generated surface (removing its Construction History) to the relative position r0 2.158593335574. In this position, move the pivot again, now from the surface to the origin: a0 0 0; because when we rotate the cap, we will do it on the center of the ball (the origin of coordinates).

To get the positions of the pentagons that form the soccer ball, we calculate the offset angles with respect to the original position.

Positions of the pentagons at the poles of the sphere have their center shifted by a 90º angle, in the X coordinate. Duplicate the surface of the first pentagon, rotating it 90º over the X axis.

The position of the rest of pentagons is rotated, with respect to the X coordinate, an angle proportional to the apothem a' of the pentagon, plus one half the apothem a of the hexagon; and over the Z axis an angle equivalent to 3/4 the distance between the hexagon's vertexes; that is 1.5 · L = 1.5 · 24° = 36°. If the apothem a' of the pentagon is, by Pythagoras theorem, a'^2 = r^2 - (L'/2)^2, then a' = .6881909602356 units. The angle proportional to the apothem a', with respect to the 24º angle that corresponds to the pentagon's side length L', is a' · 24° / L' = 16.51658305º.

Rotate the surface of the second pentagon, in relative, and over the X coordinate, a r26.9088879 angle. To generate the remaining surfaces of the pentagons, on the upper hemisphere of the soccer ball, duplicate the second pentagon, with a rotation over the Z axis by 72º, and a number of 4 duplications.

The surfaces of the pentagons regarding to the lower hemisphere, we get them grouping (Edit menu, Group option) and duplicating them, with a Scale of -1 to the Z axis (Mirror).

Alien

All other considerations secondary. Crew expendable

Alien : One of the best science-fiction movies ever, along with Blade Runner, and by extension, of his director Ridley Scott. In fact, in Blade Runner (1982) there were used same visual and sound effects that were already created for Alien (1979). The production of the film was also delayed so as not to coincide with Star Wars (1977), and assess audience reactions to this new generation of "space" themed movies.

From actors themselves were hidden some aspects of the script, in order to gather their own natural reactions, as in the famous lunch scene when the alien bursts out of Kane's chest. There is a frame when Lambert goes out of shot as she fell down shocked. Great performance by Sigourney Weaver.

Both script authors, Dan O'Bannon and Ronald Shusett, were ruined until they wrote this great story, which is the influence of many other genre films such as The Thing from Another World (1951). Initially the action was placed on board of a bomber during World War II, later versioned in the short animation film B-17 (Heavy Metal, 1981). Alien's script was adapted from a novel by Alfred E. van Vogt, in 1939, The Voyage of the Space Beagle, referencing and named after the ship in which Charles Darwin sailed around the world, and who, from this trip, developed his Theory of Evolution and Natural Selection.

Dan O'Bannon, along with John Carpenter, directed years before another film, the comedy Dark Star (1974), from where they took a few ideas and scenes. For example, the alien itself, which in Dark Star was a "friendly" beach ball; the Captain Dallas or Talby, isolated in the spacecraft listening to music; querying Ash android's head or cryogenized Cmdr. Powell's seeking advice; attempt of Officer Ripley or Lieutenant Doolittle to dismantle the explosion at arguing with Mother or Bomb#20; and also the scene of the knife game trick that was also used in the Aliens sequel (James Cameron).

O'Bannon and Shusset have also written other well-known scripts such as Total Recall (1990).

Special mention of designers, among which H.R.Giger and his biomechanics, creator of the alien, which he had already drawn in his previous artwork Necronomicon IV, and J.G. "Moebius", who later repeated again with Dan O'Bannon in Blade Runner, basing on his comic book The Long Tomorrow (Métal Hurlant, 1976 - Heavy Metal, 1977). Giger and 'Moebius' have also worked in other popular films such as Tron (1982) and Dune (1976-1984); with the latter also collaborated Orson Welles, Pink Floyd and even Dalí.

There are many interesting anecdotes about the filming of the movie, like that any of the doors and rooms were not equally designed throughout the ship Nostromo; or that the Weyland-Yutani company was actually named after Scott's neighbors. But I mostly remember a comment made by its director, Ridley Scott, for whom one of his greatest concerns was that the movie would not seem outdated in the following years. And 30 years later it is still one of the best science-fiction films ever.