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- W3108894490 abstract "This study elucidated the existence of a grid -four-dimensional Escher Grid- that creates the Droste-effect using perspective in four-dimensional space, with reference to the Escher Grid that is inherent in Escher’s work “Print Gallery”. Considering that Escher Grid is two-dimensional, it is conjectured that the grid itself that creates the Droste-effect for a four-dimensional person can be created in a three-dimensional space. Since the grid can be interpreted as being based on the figure obtained by rotating and expanding the square of the Escher Grid, it is interpreted that the four-dimensional Escher Grid is a figure obtained by rotating and expanding a cube. To generate the four-dimensional Escher Grid, it was first mentioned the relationship between the nesting, perspective, and dimension, and it was revealed that there is a “vanishing line” that has an increased dimension of vanishing point. The rotation axis of the square in the Escher Grid is the vanishing point of the painting, and that point is a point symmetrical with respect to x and y on the two-dimensional plane. Considering that, it can be seen that the vanishing line, which is the axis of rotation of the four-dimensional Escher Grid, is a line symmetrical to the cube in the x, y, z directions in the three-dimensional space, that is, the body diagonal of the cube. In conclusion, it can be said that the base of the four-dimensional Escher Grid is a figure obtained by rotating and expanding a cube around the body diagonal axis." @default.
- W3108894490 created "2020-12-07" @default.
- W3108894490 creator A5087303328 @default.
- W3108894490 date "2020-12-02" @default.
- W3108894490 modified "2023-10-16" @default.
- W3108894490 title "Perspective and Illusion in Four-Dimension: Droste-Effect in Four-Dimension Based on Escher’s Work" @default.
- W3108894490 doi "https://doi.org/10.1007/978-3-030-63403-2_6" @default.
- W3108894490 hasPublicationYear "2020" @default.
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