Re: Re: Inside Klein's Doughnuts I remembered a new bottle.

Hi Venantius, hi Michael,

Michael, it would be interesting to know, how much of
the rendering artefacts in the Klein bottle
images are due to the lost smoothness of the
pasting process.

Venantius, I am not sure, wether I understood what you
meant with "hyperbolic possibilities", but if you are
interested in what happens if you apply hyperbolic
maps to images you are very welcome to visit our webpage
at www.daytar.de/art, look e.g. for In2.

nad

Venantius J Pinto wrote:

> Michael Mahan wrote:
>
> > This is a conceptual work that uses a 3-D model of a Klein bottle as
> > an image generator. A Klein bottle is a geometric object that has
> > inside and out, but consists of a single surface. Construction of
> the
> > Klein bottle is usually described as the process of deforming an
> > ordinary bottle by bending the neck around, putting it through the
> > side and connecting it to an opening in the bottom. The Klein bottle
> > is essentially a 3-D representation of a 4-d object. In building the
> > model for this project I discovered a very simple, elegant and
> > apparently new construction of a Klein bottle from two tori. Once I
> > had created the model I animated a voyage into and through it. From
> > this animation I extracted 12 frames which I combined with text to
> > create the conceptual piece which will be reproduced as a series of
> > limited edition archival quality prints. This work is part of a
> > metaproject, Hyperobjects, which examines 3-D representations of 4-D
> > objects.
>
> Miachael,
> So, I was happy to encounter your elegant solution of constructing a
> Klein from two torii. I have been looking at the Klein bottle as a
> conceptual device for coming up with drawings that convey emotional
> states — as appear in Kakfka’s Metamorphosis. The idea being to
> distort humans as well as the reality around them using the klein
> bottle or other hyperbolic possibilities and approaches as a starting
> point.
>
> I am not a mathematician(a lowly artist) but can usually figure out
> images when I see one and then take off from there or come up with
> other shapes.
>
> Hopefully in the future, I will encounter more of your work. Also, I
> would appreciate it very much, if you do happen to know of a good yet
> lucid book — or topics that may relate to what I say above.
>
> Regards,
> Venantius J Pinto