## Archive for June 19th, 2008

### La done butterfly

Thursday, June 19th, 2008

The above image displays a visualization of the socalled blancmange curve at various iteration steps and with a slightly randomized sawtooth function. The blancmange curve -not to confuse with the blancmange pudding- is -like e.g. also the devils staircase a socalled pathological function, i.e. a function which displays a counterintuitive behaviour. In order to obtain the blancmangecurve one sums up little sawteet h which get smaller and smaller. However also if the sawteeth are getting in the end infinitely small this particular curve will never be smooth.

mathematical subleties after the more