This is a Quality image. Click here for more information.

File:Sierpinski-Pyramide Spitze 8K OpenCL HQ 20200221 002.png

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Original file ‎(8,000 × 8,000 pixels, file size: 32.15 MB, MIME type: image/png)

Captions

Captions

Sierpinski pyramid standing on its peak. Its fractal's shadow is a Sierpinski triangle.

Summary[edit]

Description
Deutsch: Eine auf der Spitze stehende Sierpinski-Pyramide. Die Lichtposition ist so gewählt, dass die Sierpinski-Pyramide einen Schatten auf eine 2D-Fläche wirft, der dem Sierpinski-Dreieck ähnelt. Dies drückt eine Sinnesverwandtschaft aus. Die Tatsache, dass höhere Sierpinski-Fraktale auf einer niedrigdimensionalen Variante basieren, lässt sich so bestärken. Durch gezielte Anwendung lässt sich das Fraktal auf seinen niedrigdimensionalen Ursprung kompaktifizieren (typischerweise durch Schattenwurf oder Querschnitt durch das Fraktal durch den Ursprung (bspw. schneiden durch die XY-Ebene)). Dies funktioniert auch mit der Mandelbulb, durch die man die Mandelbrot-Menge "heraussuchen" kann. Die Grundfläche der Sierpinski-Pyramide, die parallel zum Boden ist, ist ein Sierpinski-Dreieck. Die Lichtquelle ist schräg über und hinter dem Betrachter. Erstellt mit mandelbulber2. Das Besondere an dem Bild ist, dass es den Zusammenhang zwischen Sierpinski-Dreieck (2D) und dreidimensionalem Äquivalent in einem einzigen Bild (inkl. textueller Erklärung) zeigt. Die "anderen Versionen" zeigen weitere Visualisierungen und weiter visuelle Informationen zu diesem Sachverhalt.
English: A Sierpinski pyramid standing on its peak. The main light source position is set like this, to offer a Sierpinski triangle-like shadow, that is cursed by the pyramid. This shows, that these both structures have something in common. If you use special properties of a higher dimensional fractal, you can find out its lower dimensional origin. This might work with the shadow of the fractal (like here) oder with a proper cut through the fractal (e.g. the Mandelbulb). Created with mandelbulber2. The surface area of the pyramid that is parallel to the bottom, is a Sierpinski triangle. The main light is behind and over the viewer. The interesting part of the image is the context of the Sierpinski triangle (2D) an its threedimensional equivalent shown in one image (with explaination). The "other versions" show more visualizations (and special properties) and more visual information (like symmetry).
Date
Source Own work
Author PantheraLeo1359531
Other versions File:Sierpinski tetrahedron.jpg: Früheres Rendering eines anderen Nutzers/An older rendering of another user.
Simplified
Einfachere Ausführung

Visualisierung der Grundlinien der zum Boden parallelen Grundfläche der Pyramide mit Verhältnis zum Schatten. Korrespondiert mit anderen RGB-Linien-Bild.

Visualization, of what line curses what line on the bottom (shadow). Line of same colors belong together. Corresponds with other RGB lines image.

Panorama with position of main light
Panorama mit Position der Lichtquelle

Sierpinski pyramid with a symmetrical order of colored triangles.
Sierpinski-Pyramide mit symmetrisch angeordneten Farbdreiecken.

Markant lines of the Sierpinski pyramid.
Markante Linien der Sierpinski-Pyramide.

Sierpinski pyramid, as seen from the other side. Shadow nearer to viewer than fractal.
Sierpinski-Pyramide, gesehen von der anderen Seite.

Visualization, of what line curses what line on the bottom (shadow). Correspondents with other RGB lines image.
Visualisierung der Grundlinien der zum Boden parallelen Grundfläche der Pyramide mit Verhältnis zum Schatten.

Approximately identical view, when viewer looks from the position of light onto Sierpinski pyramid. The pitch is 45°.
Ungefähre Darstellung von Position Licht = Position Kamera und Pitch=45°

Sierpinski pyramid animation.
Sierpinski-Pyramide-Animation. Am Ende sieht man die Grundfläche (parallel zum Boden), die identisch mit dem Sierpinski-Dreieck ist.


Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

Der Urheber des Werkes, User:PantheraLeo1359531, verzichtet auf den Zusatz share alike. --PantheraLeo1359531 😺 (talk) 10:06, 21 February 2020 (UTC)

Annotations
InfoField
This image is annotated: View the annotations at Commons

Quality image

This image has been assessed using the Quality image guidelines and is considered a Quality image.

العربية ∙ جازايرية ∙ беларуская ∙ беларуская (тарашкевіца) ∙ български ∙ বাংলা ∙ català ∙ čeština ∙ Cymraeg ∙ Deutsch ∙ Schweizer Hochdeutsch ∙ Zazaki ∙ Ελληνικά ∙ English ∙ Esperanto ∙ español ∙ eesti ∙ euskara ∙ فارسی ∙ suomi ∙ français ∙ galego ∙ עברית ∙ हिन्दी ∙ hrvatski ∙ magyar ∙ հայերեն ∙ Bahasa Indonesia ∙ italiano ∙ 日本語 ∙ Jawa ∙ ქართული ∙ 한국어 ∙ kurdî ∙ Lëtzebuergesch ∙ lietuvių ∙ македонски ∙ മലയാളം ∙ मराठी ∙ Bahasa Melayu ∙ Nederlands ∙ Norfuk / Pitkern ∙ polski ∙ português ∙ português do Brasil ∙ rumantsch ∙ română ∙ русский ∙ sicilianu ∙ slovenčina ∙ slovenščina ∙ shqip ∙ српски / srpski ∙ svenska ∙ தமிழ் ∙ తెలుగు ∙ ไทย ∙ Tagalog ∙ Türkçe ∙ toki pona ∙ українська ∙ vèneto ∙ Tiếng Việt ∙ 中文 ∙ 中文（简体） ∙ 中文（繁體） ∙ +/−

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current18:40, 24 February 2020Thumbnail for version as of 18:40, 24 February 20208,000 × 8,000 (32.15 MB)PantheraLeo1359531 (talk | contribs)Reflexiven Boden hinzugefügt, Reihung von Sierpinski-Pyramiden entlang der X- und Z-Richtung. Mirroring bottom added, row of Sierpinski pyramids in X- and Z axis.
10:02, 21 February 2020Thumbnail for version as of 10:02, 21 February 20208,000 × 8,000 (29.36 MB)PantheraLeo1359531 (talk | contribs)Small image.
09:58, 21 February 2020Thumbnail for version as of 09:58, 21 February 20208,000 × 8,000 (87.42 MB)PantheraLeo1359531 (talk | contribs)Schnelle Umgebungsverdeckungsberechnung.
09:57, 21 February 2020Thumbnail for version as of 09:57, 21 February 20208,000 × 8,000 (22.29 MB)PantheraLeo1359531 (talk | contribs)Diffuse-Kanal
09:56, 21 February 2020Thumbnail for version as of 09:56, 21 February 20208,000 × 8,000 (10.39 MB)PantheraLeo1359531 (talk | contribs)ZBuffer/Tiefenkarte.
09:31, 21 February 2020Thumbnail for version as of 09:31, 21 February 20208,000 × 8,000 (123.68 MB)PantheraLeo1359531 (talk | contribs)User created page with UploadWizard

You cannot overwrite this file.

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Sierpinski-Pyramide_Spitze_8K_OpenCL_HQ_20200221_002.png&oldid=704331033"