Metacube – Gigacube

In communication, the term means to the plication in 3D of an informative 2D surface in order to obtain a compact disposition of information in digital devices. Some authors[1] refer to this plication as the reiterated interlacement or multi- interlacement of an informative surface. An informative surface is the result of exposing the required information in an only one visual plane. The transit for the exposed information respects an orthogonal direction. That informative surface is defined in base on the informative unit of surface ${\displaystyle a_{ij}}$ ( normally square ) whose amount of information is defined ad hoc.

Presentation of the information

Metacube arises from the need to communicate and store the information in devices of increasingly smaller screen. This fact has influenced in other basic parameter, the portability. We can view the information where and when we desire. This fact, is being transcendental in time to design the presentation of the information, because it obligates to iconography and to group a lot more (simple symbols or complexer combinatorials), this is, impels to synthesize concepts to expose them in a relatively small screen. Also, has been important the “touching” incorporation as interaction element “user-interface” because it establishes simpler protocols and obligates to synthesize the distribution of the information. Some investigators usually define the 2.0 era (and its devices) precisely for what the new design of the information involves in reduced screen. The 2.0 refers to the size, the portability and today, refers to the possibility to manage the transfer of information without physical anchors to networks through 3G devices of reduced dimensions.

The “presentation of the information” (screen interface) must accomplish three basic requirements adjusted in three parameters:

• FORM: the aspect of the base in which is presented the information must be compact and codable ( density and comprehension of the screen information).
• SIZE: the proposed route is initially infinite ( the infinite amount of information is limited only by the memory).
• USABILITY: the ways and possible directions to transit through, must be easily and intuitively understood (the “touching” that finally is proposed to respond to that aim, must count with intelligible and codable protocols ).

A (rentable) solution at the proposed challenge for the combination of these three parameters was developed by Josep A. Esteve in 2011 with a configuration of interface, that was called Metacube.[2] The extensive Metacube theory is being developed in the CETEC where is tried to create a theory framework for an information model of synthesis applied to the interfaces of 2.0 devices .

The construct plot in which is based the Metacube concept, is exposed in the sections below:

Informative surface

We start from a determined amount of information. We can express this amount in number of “information screens”.

All screen information is shown as a 2D surface where each cell (view Image 1) is an “information unit” (text, image, sound,...). This cell is represented by ${\displaystyle a_{ij}}$, in mode of the element of a matrix, where ${\displaystyle i,j}$∈ℤ+ (are entire positive numbers) and to the set (all the information surface) is denoted by ${\displaystyle \{a_{ij}\}}$. An informative surface is an infinite set of units-cells of information.

Image 1.

This surface can be as big as you desire. In practical effects the storing of the information only depends on the memory of the involved device .

We define the concept “informative surface operator”[3] to all made action on the information surface, or in one of its cells in order to generate a change in the information presentation. This change can be structural, apparent, virtual, etc...

Is defined the operator k that corresponds to the “cell jump[4] concept. This action is the pass of one cell to one of the for cell-borderline below, as is indicated in the image 2.

Image 2.

We have a set of elements with an operator, this is ${\displaystyle (\{a_{ij}\},k)}$.

Metacube

Assuming the 2.0 needs explicited before, to which were necessary to respond with solving, is proceeded to “fold” the structure “informative surface” that has been defined and we transformer it in a 3D element, this is, a cube. This cube, is what we have called Metacube, because it has infinite faces ( or the amount that are desired to define). In terms of a mentally supposed tridimensional representation in the cognitive process of the user, Metacube does not let of representing itself as a polyhedron of six appereant faces, because it maintains the formally of a one traditional cube.

Every frontal face, which is shown in the screen interface, is one of the cells ${\displaystyle \{a_{ij}\}}$ of the informative surface ${\displaystyle (\{a_{ij}\},k)}$ and every “face jump” pass to be a “rotation” of central axis ( vertical or horizontal ) showing the informative content anterior or posterior of the cube face of infinite faces, as is shown in the images 3 and 4.

Image 3. Cell jump (2D)
Image 4. Face rotation of Metacube (3D)

The structure ${\displaystyle (\{a_{ij}\},k)}$ is denominated METACUBE.

It is obvious that Metacube allows to store the amount of information that we desire (each face shows the information that we have put in the Metacube), to select with the “touching” the information that we want (search).

Gigacube

In order to increase the organizational capacity and therefore magnificate the Metacube structure, is defined the concept called GIGACUBE. A Gigacube is a Metacube of Metacubes. It is the association of a Metacube to each face of a Metacube, multiplying exponentially the organizational capacity of the Gigacube structure. In fact, the growing is logarithmic and can be regulated at will. It could be said that all the information of the universe, could be presented to the user through a Gigacube interface.

Is denominated Metacube of Base or Metacube of level 1, the first Metacube that we find in the interface.

Metacubes associated to the faces of the Metacube of level 1, are denominated Metacubes of level 2 and so on.

The capacity of one Gigacube, depends on the magnitude (number of faces of the Metacubes of superior levels) associated to the faces of the metacube of level 1 and successively the metacubes of distinc level that are associated.

To active the Metacube associated to the face of one Metacube of base ( or inferior) we use the operator D that realize the action that we know as “Double Click” .Is understood that the double clic actives the emergent metacube.

The structure ${\displaystyle (\{a_{ij}\},k,D)}$ is denominated GIGACUBE.

Gigacube form in the screen interface of a digital device is shown in the image 5.

Image 5. Left,Metacube Appearance. Right, Gigacubo Appearance

The Gigacube structure ${\displaystyle (\{a_{ij}\},k,D)}$ complies the three requirements for the correct “presentation of the information” in the reduced interface. It remains to establish the “ compare information” protocol.

To compare information (units) must be exposed some Metacube faces at the same time in the screen interface. For this, is defined the operator ${\displaystyle {\overrightarrow {T}}}$ that acts as “timer-touching” on the interface of Metacube. This operator corresponds to the action for which the user, keeping the “touch” during a period of time larger than normally, actives the Metacube as screen element and he can drag it around this, until place it where he desire. By this way, different Metacubes can be placed in a same interface of a same Gigacube or not ( different origin). The vectorial notation of this operator refers to its displacement capacity of the information element Metacube.

The structure ${\displaystyle (\{a_{ij}\},k,D,{\overrightarrow {T}})}$ complies the three basic requirements and, therefore, is constituted in the base of the architecture of the Gigacube concept.

This theory has been brought to practice successfully by different companies such as Tons of Toons, Esteve Animació and AppStar in the development of different App Games and App Utilities, including Zong-Ji, Pellex, Suma and Sudoku using chromenumerical Metacubes; or the PuzzKids that use iconical and chromealphabetical Metacubes.

The Gigacube structure is being used in the design of new sport informative applications.

References

1. ^ 1. Dr. J Mª Blanco in the conference “ Compactation of the Information in Metacube”. Speech of CETEC foundation. Center of Theorical Studies of the Communication. Empuriabrava, Girona, November 11th of 2011.
2. ^ 2. In works such as Nguyen, Tjoa and Wagner has been presented a Metacube Concept as the tridimensional disposition of the information (Nguyen, Tjoa y Wagner (2000) “ Conceptual Multidimensional Data Model Based on Metacube” of Nguyen, Tjoa and Wagner (T. Yakno (Ed): ADVIS 2000, LNCS, p 24-33, 2000). This approach only explains the spatial disposition of the information, transposes 2D graphic trees in a accumulate cubic in 3D, but it does not stablish the protocols of searching and comparation of the same. It is a preterit theoerical form of talking about 3D disposition of the information, for the advances in 3D infography. In the Metacube (Esteve) the information is compacted, establishing clear protocols of searching and comparation of the stored information.
3. ^ 3. The “operator” concept is generalized for any realizable action on the information and the communication of the information.
4. ^ 4. The cell jump, that more ahead we will denote it as “Face rotation [or facet]” allows the calculation of “ Informative trajectories” and the definition of “Courses of information” and how to calculate its reversibility (Thermodynamics of the information).