----- Original Message -----
**From:** Carolyn Kunin
**Sent:** Sunday, September 28, 2003 10:28 AM
**Subject:** Re: MARY KRIMMEL ON FRACTALS

VN may have known about fractals even without any personal relationship with Mandelbrot. The idea goes back earlier in the 20th century to another Polish mathematician named Sierpinski and before that, as Jansy asks, it is definitely related to the logarithmic spiral. Like other fractals, the spiral continues unchanged no matter how closely you look at it. It recedes infinitely at the same level of detail. I am not describing it very well, but if you are familiar with the phenomenon you will know what I am trying to say.

I have seen the frac-tail reference, and there does not appear to be any mathematical allusion there. Jansy's find may be an optical illusion, but it has turned out to be one with interesting repercussions. I intend to look into the possibility (planted in my memory of Tom Stoppard's play

Also interesting to find that a Summer workshop on Fractals included literary examples of fractals drawn from two works of VN's,

Carolyn

> EDNOTE. NABOKV-L thanks Mary Krimmel for her discriminating and informative

> note.

> ----- Original Message -----

> From: Mary Krimmel

> Message requiring your approval (29 lines) ------------------ Benoit

> Mandelbrot claims the coining of the term "fractal" for a collection of

> certain mathematical sets. He explains this in "Fractals: Form, Chance, and

> Dimension", published in 1977, a "much modified and augmented second version

> of 'Les objets fractals:'.. (1975)". No one disputes his claim.

>

> The explosive interest in and development of the topic depended much on the

> development of computer technology. So VN could not have known about fractals

> when he wrote Pale Fire, first published in 1962.. Surely he must have known

> something of the name and reputation of J. Bernoulli and of "Math", but

> putting the golden rectangles into the collection of connotations of the

> lemniscate of line 137 is too much of a stretch.

>

> The rectangles are not related to the findings about fractals - at least not

> in any but the most distant way.

>

> Mary Krimmel

>

> Jansy asked:

>

> "In the Post-Script that VN added to "Lolita" he speaks about enchanters and

> he uses the word "fractails". I wonder if he could also be making a reference

> there to the modern mathematical discoveries concerning 'fractals' ?

> "Would those 'smaller and smaller golden rectangles' of Bernouilli´s

> logarithmic spiral -brought up by C. Kunin - be in any way related to the

> findings about fractals? Would VN be familiar with Math, Bernouilli and

> Fractal theory? "

>

>