Kochsim.gif (200 × 100 Pixel, Dateigröße: 4 KB, MIME-Typ: image/gif, Endlosschleife, 9 Bilder, 0,9 s)
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BeschreibungKochsim.gif | A Koch curve has an infinitely repeating self-similarity when it is magnified. |
Datum | |
Quelle | en:Image:Kochsim.gif |
Urheber | en:User:Cuddlyable3 |
Genehmigung (Weiternutzung dieser Datei) |
PD-self |
I made this animation Cuddlyable3 15:36, 13 March 2007 (UTC) The Koch curve, in its fully (infinitely) iterated form is not a line that anyone has ever seen! That is to say, it is not like any of the lines that we are familiar with in Euclidean geometry because it somehow spans a finite distance while being infinitely long. The cross-section of an ordinary 2-D line is a point, but the cross-section of the Koch curve would have to be a probability distribution. That makes displaying the Koch curve challenging and we may need to rethink what we mean by aliasing error. The quantising imposed to make this animation is:
Each of the above is a potential source of aliasing error, but I think the dominant cause of comments about this is the restricted colour scale. Any pixel that the Koch "distribution" touches, no matter how slightly, is painted black. It is that simple.
Other details of this animation:
Finally, I judiciously panned the view of the sequence so the last frame smoothly recycles to the first frame i.e. the center of the curve seems to remain still. Although that gives a nice subjective effect, it may encourage a misinterpretation that forms are being emitted from the center. What you see is really just a zoom and pan view of a strange but static "self-similar" object.Cuddlyable3 19:14, 7 May 2007 (UTC)
^I got rid of the deprecated tag, and I'll add this tag. Plus, nominated for featured.Temperalxy 19:12, 6 May 2007 (UTC)
See my Discussion page for some variations of this animation. Cuddlyable3 19:07, 2 June 2007 (UTC)
Public domainPublic domainfalsefalse |
Ich, der Urheberrechtsinhaber dieses Werkes, veröffentliche es als gemeinfrei. Dies gilt weltweit. In manchen Staaten könnte dies rechtlich nicht möglich sein. Sofern dies der Fall ist: Ich gewähre jedem das bedingungslose Recht, dieses Werk für jedweden Zweck zu nutzen, es sei denn, Bedingungen sind gesetzlich erforderlich. |
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aktuell | 09:06, 7. Apr. 2007 | 200 × 100 (4 KB) | wikimediacommons>Lerdsuwa | {{Information |Description=A Koch curve has an infinitely repeating self-similarity when it is magnified. |Source=en:Image:Kochsim.gif |Date=13 March 2007 |Author=en:User:Cuddlyable3 |Permission=PD-self |other_versions= }} |
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