WO2000045914A1 - Flat pattern consisting of hexagonal tiles with deformed edges - Google Patents

Abstract

The invention relates to a set or a plurality of 14 different tiles which differ in type, and notably in colour, between which a dividing line can extend and which can be assembled in the manner of a jigsaw puzzle to form a flat pattern. The shape of the individual tiles is based on regular hexagons whose edges can be deformed in a particular manner. The shape and number of different types of edges is determined on the basis of a mathematical model and based on the presence or absence of a colour transition or a dividing line to adjacent tiles. In this way eight different edges are created from which six pairs can be formed. The tiles provided for in the invention oblige a user to fit said tiles together correctly and at the same time permit the creation of a multitude of different flat tiling patterns. The invention can be used as a jigsaw puzzle or flat surface cover.

Description

Surface pattern from edge-deformed hexagonal building blocks

description

The invention relates to a plurality of flat building blocks, from which a surface pattern can be formed by seamlessly joining them. The individual flat building blocks are formed on the basis of a mathematical model from hexagonal basic shapes by deforming the edges. The invention can be used both as a puzzle and as a covering for a surface.

Ordinary puzzle games are characterized by the fact that the individual building blocks are put together according to a single correct system in order to obtain an image as a solution. Since there is no possibility of variation, such puzzle games are mostly used only once. However, such lay-on or puzzle games have long been known, which consist of a set of different building blocks, which can be joined together in different ways to form different shapes or patterns. Among these is, for example, the long-known domino game, the original shape of which consists of a set of regular hexagons, each of which is divided into six equally large circumferential sections of different colors and different order of colors, and which must be put together according to the colors.

In another domino game according to US Pat. No. 1,362,318, a number of points from 1 to 6 is printed on each of the six circumferential sections, and the goal is to put the domino building blocks together in such a way that the total number of points of the circumferential sections of adjacent dominoes is 7 .

These domino games are suitable as betting games between two or more people and, in contrast to homely puzzle a variable game development. However, the pattern that is formed is not flat, but proceeds along a possibly winding and branched line. The resulting colored patterns are still more or less random, since they are not subject to any sort of order. Compared to the ordinary puzzle, there is a disadvantage in that the resulting surface patterns are not mechanically secured against slipping.

Furthermore, a game called Tantrix has become known from New Zealand, which consists of a set of 56 hexagonal building blocks, which are printed in different ways with lines of four different colors and from which complex color patterns can be created by laying them flat and connecting them . However, these surface patterns formed are not secured against slipping as a result of the regular hexagons which have not changed in their external shape.

However, such puzzle games are also known, the building blocks of which have emerged from hexagonal basic shapes by modifying or deforming their outer straight edges. Such a game is known for example from US Pat. No. 5,481,841. It consists of a set of eight different axisymmetric building blocks, which are formed by replacing three consecutive edges of a regular hexagon with certain asymmetrical and curved edge profiles and mirroring the resulting structure on the opposite hexagon edges. With these building blocks, it is possible to assemble a surface, which is secured against slipping. This publication also mentions that the building blocks can be of different colors, so that a colored patchwork can be produced by joining these building blocks together. However, there is no technical teaching for how the building blocks must be shaped so that orderly and aesthetically appealing color structures of the surface pattern are created by joining the building blocks.

Accordingly, it is an object of the present invention to provide a set or a plurality of building blocks in which, in a targeted or untargeted manner, ordered and aesthetically appealing structures are produced by joining the individual building blocks.

To achieve this object, the invention describes a set or a plurality of 14 different building blocks which have different types of surfaces, in particular different colors and / or surfaces (e.g. structures / materials) and / or boundary lines running between the types of surfaces, and which are puzzle-like to form a surface pattern can be put together. The shape of the individual building blocks results from regular hexagons, the edges of which are deformed in a certain way. The shape and number of different edges is determined on the basis of a mathematical model based on the presence or absence of one

Color / type transition and / or a boundary line to the neighboring block is determined. In this way 8 different edges are created, between which 6 pairs can be formed. The building blocks according to the invention force them to be put on correctly when they are put together, so that a variety of conceivable surface patterns can be generated which have an ordered internal structure in common. The invention can be used as a puzzle or as a surface covering.

The invention solves the problem in that the external design of the individual blocks is linked in a certain way with their surface design. This link is determined by the mathematical model in question. As a result, there are exactly 14 different building blocks that emerge from regular hexagons by deforming their hexagon edges. There are also exactly 8 different edge shapes and exactly 6 possible pairings between these. The edge shapes correspond to the respective (e.g. colored) surface transition and / or the drawing of the boundary line on them, so that when they are put together, a so-called correct application is forced, i.e. an application in which an orderly structure results automatically. In this way it is achieved that when assembling a variety of ordered surface patterns is generated by itself.

The invention and in particular the mathematical model on which it is based and an exemplary embodiment for the shaping of the edges are explained in more detail below in connection with the drawings.

Show it:

1 shows a hexagonal honeycomb grid colored randomly with two colors;

FIG. 2 shows the hexagonal honeycomb grid from FIG. 1 with a solid boundary line;

3 shows the 14 hexagon classes with the drawing of the boundary line and the binary number (0, 1) indicating the color change;

4 shows the 8 types of hexagon sides determined by the drawings of the boundary line;

5 shows the page assignment of the 14 types of hexagon;

6 shows the 6 only possible pair formations;

7 shows a graphical representation of the possible transitions;

8 shows the 8 different edge shapes in an exemplary shape; 9A and 9B show the 14 different building blocks in an exemplary shape;

FIG. 10 shows a surface pattern corresponding to FIG. 2 produced by placing a number of building blocks of the set according to FIG. 9A next to one another.

The mathematical model on which the present invention is based assumes that - as shown in FIG. 1 - a hexagonal grid in the manner of a map is filled with two different colors. For each individual hexagon edge of a hexagon, a clear statement can be made as to whether or not a color change is taking place for the directly opposite hexagon. This can be done with the binary numbers

0: no color change and 1: color change

be marked.

The neighborhood relationship of a hexagon to its six neighbors can thus be identified by a six-digit binary number, in which each individual binary position is assigned to a specific hexagon edge. For example, the first binary digit corresponds to the upper hexagon edge and the other binary digits continue to correspond clockwise to the other hexagonal edges.

According to Table 1 in the appendix, there are exactly 14 different types (classes) of components or chips that result from dividing the 64 binary numbers with a length of 6 bits so that two binary numbers each belong to the same class, if they can be converted into one another by a cyclical shift. A cyclical shift corresponds to only one rotation of one Hexagons through which the hexagon does not change qualitatively.

If - as in Fig. 2 - the color change in the honeycomb grid is underlined by a solid border line, then the drawing of this border line on the individual hexagon determines its affiliation to one of the 14 neighborhood classes.

In Fig. 3 the 14 hexagon classes are shown in the picture, with the boundary line being drawn on each module, which results depending on whether or not there is a color change to the neighboring hexagon. In addition, the neighborhood relationship to the neighboring hexagon is marked on each side with the corresponding binary number (0, 1).

Thanks to the pure hexagonal building blocks described so far with the 14 different lines of the borderline shown, all two-color maps can now be drawn. However, they would have the disadvantage that the shapes would slip too easily; furthermore, laying errors would not be prevented automatically and would often only be discovered much later.

For this reason, another property of the 14 hexagon classes is used: by developing the drawing of a single hexagon side of a building block, the neighborhood relationship on this side is clear

- to a hexagon which lies opposite the edge on the left-hand side, to a hexagon directly opposite and to a hexagon which lies opposite the edge on the right-hand side

fixed For a hexagon side, all 8 relationships are possible, which are indicated by the letters A - H in Table 2 in the appendix. As shown in FIG. 4, there are exactly 8 different types of hexagon sides in all 14 types of hexagon.

Fig. 5 shows the assignment of the sides of the 14 hexagon types with the page types A - H.

Each of the 14 hexagon classes is one by type

Side completely defines the type of the adjacent side of the neighboring hexagon directly opposite. In fact, only the 6 pairs shown in Fig. 6 are possible.

With a suitable puzzle-like design of the hexagon sides it can be achieved that - similar to a 2-dimensional syntax - correct application is forced. There is also the effect that the surface patterns are secured against slipping.

The possible transitions from one side to the neighboring side in a clockwise direction are shown by the graph in Fig. 7.

The 8 page types must therefore be selected in such a way that they can be put together in pairs thanks to the 6 pairs (A-A, B-E, C-H, D-D, F-F, G-G). There are in principle an infinite variety of possibilities for the formation of these 8 page types. FIG. 8 shows an example of the deformed hexagon edge and the original course of the two adjacent hexagon edges; the boundary line printed or painted on the respective module is also shown.

The use of the edges according to FIG. 8 leads to the block shapes according to FIG. 9A, in which the blocks 1 to 14 are shown in their complete state. It should be emphasized again that the edge shapes chosen here according to FIG. 8 are not mandatory. However, the freedom in determining the chip edges lies solely in the shape of the edge types A - H, and here one half is determined by the other: - The point-symmetrical types A, D, F, G are through an edge half fixed and B and E bez. C and H are mutually determined.

For clarification, the blocks 1 to 14 are shown in FIG. 9B on the basis of modified edge shapes A - H.

A surface pattern is shown as an example in FIG.

There are relatively high demands on the accuracy of the edge design, because, in contrast to the usual puzzle, an edge must not only match the edge from which it is embossed, but also other complementary edge shapes.

In the exemplary embodiment shown, a boundary line is used for the optical separation of different surface types. The areas on either side of the border line can then have the same color or different colors. In principle, however, the boundary line can also be dispensed with; if two blocks of different colors are then placed next to each other, the border is identical to the edge of the blocks.

A strong internal structure is common to all surface patterns produced with the present invention. They are therefore symbolic of complex processes in the real world that are currently being investigated in many scientific disciplines. The game presented here could be a symbol for the emergence of forms in the world or for syntactic rules, for example, the blueprint for a gene is subject to. With regard to applications, the present invention can be used, for example, as a domino game in accordance with modified game rules. As a betting game for two players or parties, the invention can be used, for example, according to the following basic rules: each party is assigned a color, and it is alternately created from a common pile. A country may only consist of chips of one color and a change to another color must take place each time it crosses a border. The winner is the party that ultimately owns the country with the most chips. Such rules can be modified in various ways, for example by specifying a defined starting pattern or a frame in which the game is played.

The invention can also be used as a pure puzzle game, with the focus on the joy of the resulting shapes. The surface pattern shown in Fig. 2 was created, for example, by a random process.

Furthermore, the invention can be used as a modular system, and images and patterns can be placed with any number of colors.

In addition, the chip shapes are also well suited for the structural design of wall and floor surfaces, for example as tiles or composite paving stones.

Table 1

Tabelle 2

Table 2

Claims

claims 1. A plurality or set of two-dimensional building blocks from which a surface pattern can be formed by seamlessly joining them, whereby - The surface pattern has different types of surfaces, which can be distinguished from one another by boundary lines running across the surface pattern and / or by different colors, structures or other features, and the surface building blocks are formed by deforming the six edges of a regular hexagon in a certain way are characterized in that - 14 different types of building blocks are contained in the set and are formed by the deformation of one of the six edges of a building block being determined by whether, during a transition to another building block, which lies opposite the edge on the left-hand side, in the case of a transition to another building block, which lies opposite the edge to be deformed, in the case of a transition to another building block, which lies opposite the edge on the right-hand side, the surface type changes (1) or remains constant (0), from which the eight different edge shapes are formed by forming 3-digit binary numbers (000) (A); (100) (B); (010) (C); (110) (D); (001) (E); (101) (F); (011) (G); (111) (H) result for a hexagon edge, and the edge shapes can be combined in pairs by the following 6 pairs: (100) - (001) B - E (000) - (000) A - A (101) - (101 ) F - F (010) - (111) C - H (110) - (110) D - D (011) - (011) G - G. A plurality of two-dimensional building blocks according to claim 1, so that the boundary line drawn on two edge shapes that can be joined together and / or the boundary between the surface types in the assembled state has a continuous or flush course. 3. A plurality of flat building blocks according to claim 1, d a d u r c h g e k e n n z e i c h n e t that by shaping projections and recesses in each case an edge profile is generated, which ensures a positive holding together of building blocks. 4. A plurality of flat building blocks according to claim 1, so that the building blocks according to the possible assignments of their edges with "surface type remains constant" (0) or "Surface type changes" (1) and can be divided into 14 classes by summarizing the assignments that can be converted into one another by rotating the building blocks. 5. surface pattern, which is assembled from a number of building blocks from a set according to one of claims 1 to 4. 6. Puzzle game with a plurality of flat building blocks according to one of claims 1 to 4. 7. mosaic, which is assembled from a number of building blocks from a set according to one of claims 1 to 4.