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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
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Monthly Archives: February 2014
Playing around with the kaleidoscope
You can do things with the computer kaleidoscope you would not try with a real one. Simply look again through the kaleidoscope at an earlier image of the kaleidoscope. Using different scales I got thus:
kaleidoscope – code of the main tab
PImage inputImage,outputImage; Coordinates screenCoordinates,inputCoordinates,outputCoordinates; ColorLookup inputColor; MakeScreenImage makeScreenImage; MakeOutputImage makeOutputImage; Kaleidoscope kaleidoscope; int lastMouseX,lastMouseY; boolean dragged=false; void setup() { size(600, 600); smooth(); readImage(); int outputMagnification=1; // no magnification for blog // choose large value (about … Continue reading
putting the kaleidoscope together
We now create a rather versatile kaleidoscope. Upon starting, the program lets us choose an image file and we will look through the kaleidoscope at this image. To get a large variety of pictures we interactively manipulate the input image … Continue reading
class kaleidoscope – the code
class Kaleidoscope{ float periodX,periodY,side; float rt32=sqrt(3.)/2; float rt3=sqrt(3); int choice; final int RECTANGLE=0,THESQUARE=1,EQUITRIANGLE=2,RIGHTTRIANGLE=3; Kaleidoscope(){ } //————————————————————————— //initialization and choice of kaleidoscope // rectangular kaleidoscope void chooseRectangle(float cellWidth,float … Continue reading
class Kaleidoscope
The class Kaleidoscope collects all mappings needed to make the four periodic kaleidoscopes. We first have to create an object with kaleidoscope=new Kaleidoscope(); and then we can choose one of the kaleidoscopes. With kaleidoscope.chooseRectangle(50,120); we would have a rectangular … Continue reading
Posted in Kaleidoscopes, programming
Tagged kaleidoscope, mirror symmetry, programming, Rotational symmetry
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Geometry of kaleidoscopes with periodic images
About a year ago I explained “how to program an ideal kaleidoscope” to get the same as three mirrors put together. Often, one gets images that are not periodic. They have cut lines with a mismatch between the two sides, … Continue reading
Posted in Kaleidoscopes
Tagged Geometry, kaleidoscope, mirror symmetry, period doubling, periodic images, Rotational symmetry
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