File:Zusammenhang euklidisch fraktal 20200306.png

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Description	Deutsch: In dem Bild sind zwei Körper derselben Grundform zu sehen (2 Kuben). Jedoch ist der linke Körper ein euklidischer Körper, und er hat eine ganzzahlige Dimension (3 Dimensionen: Länge, Breite, Tiefe). Ein Reinzoomen in diesen Körper offenbart keine neuen Details oder Strukturen. Der rechte Körper ist ein Körper der fraktalen Geometrie, da er sowohl eine gebrochene Dimension (Hausdorff-Dimension), als auch echte Selbstähnlichkeit hat. Zusammenhang: Wenn man annimmt, dass die längste Kante des Mengerschwammes eine Längeneinheit (1 LE) lang ist, so kann theoretisch dieser (Menger-Schwamm) aus (unendlich vielen) Kuben bestehen, wobei jeder Kubus eine Kantenlänge von dem Kehrwert von ω (Zahl mit unendlich hohem Wert) hat. So würde eine 1-dimensionale Reihung von unendlich vielen Kuben die Kantenlänge des Mengerschwammes ergeben (Kehrwert von einem unendlich hohen Wert * unendlich hoher Wert = 1). Aus den Kuben dieser Ausdehnung ließe sich ein Menger-Schwamm entwickeln, der idealtypisch ist. Dies funktioniert auch andersherum: Man kann einen Menger-Schwamm durch Kuben konstruieren, indem man subtraktiv arbeitet. Wenn man kubische Volumina gezielt aus einem Kubus entfernt, kann man einen Menger-Schwamm erstellen. Der Kubus wird auch als mathematisches Primitiv bezeichnet. Erstellt mit mandelbulber2. English: This image shows two bodys of the same basic form (2 cubes). The left body is an euclidic one, and has exactly 3 dimensions. A zoom-in into this body doesn't show any new (smaller) structures. The right body is a fractal one and has a Hausdorff dimension, and also self-similarity. Context: Assuming, that the furthest edge of the Menger sponge is one length unit long, the Menger sponge can be made out of (theoretically) an infinite amount of cubes. In this case, one cube must have an edge length of 1/ω (ω is a number with infinite amount). A row of an infinite amount of cubes leads to one unit length, the same length like the Menger sponge's edge (ω * (1/ω)= 1 -> 1 length unit). This curses an ideal (Menger sponge after every iteration or deepest iteration depth) Menger sponge. This also works subtractive. If you have a cube, you can remove smaller cube-shaped volumina from the original cube. A targeted removing process can also lead to a Menger sponge. The cube is also called as mathematical primitive. Created with mandelbulber2.
Date	6 March 2020, 09:16:25
Source	Own work
Author	PantheraLeo1359531
Other versions	File:Menger-Schwamm-Reihe.jpg: Korrespondierende Datei

FRACT-Datei:

Mandelbulber settings file
version 2.20
only modified parameters

[main_parameters] ambient_occlusion_enabled true; ambient_occlusion_mode 1; ambient_occlusion_quality 10; background_3_colors_enable false; background_color_1 0000 0000 0000; camera 0 -4,5 0; camera_distance_to_target 4,5; camera_rotation 0 0 0; camera_top 0 0 1; DE_factor 0,5; flight_last_to_render 99999; formula_1 10; fractal_position 1,5 0 0; glow_enabled false; hdr true; image_height 4500; image_proportion 4; image_width 8000; keyframe_last_to_render 0; mat1_file_color_texture C:\Program Files\Mandelbulber2\textures\colour palette.jpg; mat1_is_defined true; mat1_surface_color_gradient 0 7b00ff 908 000fff 1817 0097fe 2727 00feda 3635 00ff53 4545 34ff01 5454 bdfe00 6363 ffb400 7271 ff2801 8181 ff0164 9090 fe01f2; mat2_is_defined true; mat2_surface_color 2e00 ff00 0000; mat2_use_colors_from_palette false; primitive_box_1_enabled true; primitive_box_1_material_id 2; primitive_box_1_position -1,5 0 0; primitive_box_1_size 2 2 2; raytraced_reflections true; [fractal_1] IFS_abs_x true; IFS_abs_y true; IFS_abs_z true; IFS_direction_5 1 -1 0; IFS_direction_6 1 0 -1; IFS_direction_7 0 1 -1; IFS_enabled_5 true; IFS_enabled_6 true; IFS_enabled_7 true; IFS_menger_sponge_mode true; IFS_offset 1 1 1; IFS_scale 3;

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	Date/Time	Dimensions	User	Comment
current	11:55, 6 March 2020	8,000 × 4,500 (54.25 MB)	PantheraLeo1359531 (talk \| contribs)	Reverted to version as of 09:21, 6 March 2020 (UTC)
	11:55, 6 March 2020	8,000 × 4,500 (4.98 MB)	PantheraLeo1359531 (talk \| contribs)	Tiefenkarte
	11:54, 6 March 2020	8,000 × 4,500 (26.73 MB)	PantheraLeo1359531 (talk \| contribs)	Normalen-Kanal
	11:53, 6 March 2020	8,000 × 4,500 (30.4 MB)	PantheraLeo1359531 (talk \| contribs)	Specular (Glanz)-Kanal
	11:52, 6 March 2020	8,000 × 4,500 (7.6 MB)	PantheraLeo1359531 (talk \| contribs)	Diffuse-Kanal
	11:50, 6 March 2020	8,000 × 4,500 (66.3 MB)	PantheraLeo1359531 (talk \| contribs)	World-Kanal
	11:48, 6 March 2020	8,000 × 4,500 (26.51 MB)	PantheraLeo1359531 (talk \| contribs)	NormalWorld-Kanal
	09:21, 6 March 2020	8,000 × 4,500 (54.25 MB)	PantheraLeo1359531 (talk \| contribs)	Uploaded own work with UploadWizard