Keywords: Kochsim.gif About this image 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 Resolution 200 x 100 pixels Colours Just 2 i e monochrome Time 10 frames that recycle at 10 frames/second 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 the line actually drawn is first described numerically by 4097 points i e a it is a highly developed but not infinite Koch curve This model exceeds the display resolution so much that I am sure that further Koch iteration would make no difference the points are joined in order by the Bresenham line-drawing algorithm At this scale I think I would have got exactly the same result by merely plotting the points because there is no line span long enough for the B algorithm to paint intermediate points but now you know what I told the computer to do the animation was assembled using The Gimp software into a gif file of only 4 331 bytes 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 Temperal<span style color red ><small><sup>xy</sup></small></span> 19 12 6 May 2007 UTC See my Discussion page for some variations of this animation Cuddlyable3 19 07 2 June 2007 UTC Koch curves Animations of Fractal zoom |