this is an interesting threat. i always thought julia had no idea how his sets would look like. and the effort to get a short glance on these sets can't be rated high enough - his only resources were a slide rule and logarithmic tables. although julias ideas about the look of julia sets must have been quite rudimental.
There are other fractal investigators who explored this area geometrically, and Jakob Steiner is the main expert on the geometrical approach to space functions. He refused to go down the algebra route, and remained a synthetic geometer all his days.
to read steiner's name in conjunction with dynamic math (witch fractals are) wondered me a bit. i know steiner from constructive analysis (in fact static math). steiner is still daily task for millions of constructive engineers. steiner's theorem is essential for calculating the moment of inertia of any carrier section - mostly steel or ferroconcrete. but i see the world through the eyes of the architect - also a single-edge point of view.
thanks for broaden my horizon...
May 19, 2010, 03:11:42 PM
Deep julia morphing like as the julia set at 0+1i
Ultra Deep Mandelbrot
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