
Recent Posts
Recent Comments
Archives
 December 2017
 November 2017
 September 2017
 August 2017
 July 2017
 June 2017
 May 2017
 February 2017
 January 2017
 November 2016
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
Categories
Meta
Category Archives: Selfsimilarity
Color symmetry using the length scale of the inflated lattice
I have shown some images with 2color symmetry upon rotation shown in “images of 10fold rotational …“. But the fast color changes they hacked them into small pieces. We can get better images if we use a color changing function with … Continue reading
Selfsimilarity and color modification
The Penrose tiling is selfsimilar as many other quasiperiodic tilings. It matches a copy of itself inflated by the golden ratio τ=(1+√5)/2≅1.618, see “Penrose tiling tied up in ribbons“. Noting that our quasiperiodic designs of 5fold symmetry are closely related to … Continue reading
Coloring the Julia set
The Julia set of a function f(z) in the complex plane has all points z that remain finite upon iterations of the function. In the last posts I have used expanding functions to get fractal images from iteration, as discussed … Continue reading
Posted in Fractals, Selfsimilarity, Uncategorized
Tagged fractal, Iterated function, iteration, julia set, Rotational symmetry, Selfsimilarity
Leave a comment
Rainbow colors
We can define a continuous number x of iterations needed to reach the critical radius R. Note that if the nth iteration of f(z) equals R then x=n, and if the (n1)th iteration equals R then x=n1. For values inbetween … Continue reading
Posted in Fractals, programming, Selfsimilarity
Tagged Color, fractal, fractal design, Rotational symmetry
Leave a comment
selfsimilar fractals with rotational symmetry from function iteration
I was looking at my posts of march 2013 on complex function iterations, see in particular “fractal surprise from complex function iteration” and “selfsimilar images from iterated mappings of the plane“, and I got some new ideas I want to … Continue reading
Posted in Fractals, Selfsimilarity
Tagged analysis, complex function, fractal, iteration, Rotational symmetry, Selfsimilarity
2 Comments
repeated plane mapping, anamorphosis and mirrors
The image of the last post is quite bewildering. To get a calmer and simpler image I imposed mirror symmetries on the original image. A vertical mirror line results from taking the absolute value of the xcoordinate. Similarly, I take … Continue reading
Posted in Anamorphosis, Kaleidoscopes, Selfsimilarity
Tagged anamorphosis, kaleidoscope, Selfsimilarity, translational symmetry
Leave a comment
Selfsimilar designs from repeated plane mappings and anamorphosis
I am reconsidering ideas Pickover has presented in his book “Computers, Patterns, Chaos and Beauty”. My post “Fractal surprise from complex function iteration” discusses already some aspects. Complex numbers z=x+iy represent the (x,y)plane and complex functions f(z) define a mapping … Continue reading
Posted in Anamorphosis, Selfsimilarity
Tagged anamorphosis, fractal, Selfsimilarity
Leave a comment