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What would a fully hyperbolic grid look like? The converging lines are equidistant lines. The divergent lines are geodesics (shortest distance between two points.) The bright circle is at infinity. No point inside never escapes, and no point outside ever gets inside.

From Wikipedia, the free encyclopedia: Poincaré disk with hyperbolic parallel lines "In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines are either circular arcs contained within the disk that are orthogonal to the unit circle or diameters of the unit circle. " The metric is hyperbolic. I'm not sure stereographic projection of a sphere gives the same result.

@@stereosphere On your representation, thete are 2 points where the circles come from, and disappear, those are the north and south poles of the sphere. A hyperbolic plane has no south and north poles. That circle that doesn't move is the equator.

@@Jar.Headed Look again at the circle that doesn't move. Do any of points outside the circle ever enter the circle? Do any points inside ever escape? This circle is at infinity. Contrast this with a stereographic projection of a 3D sphere. A point outside the equator smoothly transitions to a point inside the equator. The equator has no special status. Look at some of the other videos in my channel.

Yes they do, track a point of where the lines intersect as they move, very often, points will leave the circle at infinity, and if you don't mind me asking, what projection did you use?@@stereosphere

@@Jar.Headed You see that this is not a stereographic projection of a sphere in 3D space? If you set out from the center of the disk in any direction, you will never reach the circumference. In the projection, your steps will get smaller and smaller. From your perspective in hyperbolic space , your steps will remain the same size. The same thing is happening here, but the motion is more complicated. Points leave the circle at infinity and points disappear into the circle. This is the Poincare disk model, the same as used by Escher in some of his drawings. Inside the disks the polar circles are geodesics, while the other circles are equidistant curves, These are the same things in plain old Euclidean space but different things in hyperbolic space. The geodesics are circles perpendicular to the circle at infinity while the equidistants are any circle drawn through opposite points. The hemispheric model of the grid projected on a planetarium dome is really beautiful. The geodesics become vertical cross-sections and the equidistants become like the slices of an orange.

That's a good trick! Was some sort of grid enscribed on the drink bottle?

@@stereosphere no it was at school, me and my friend were just zoning out with our math grid books and made it

Good to hear from you, Randy. I'm surprised you haven't seen this. Steve and I put it together after you left. I wrote a driver to run the camera and filter wheel from the DG's rs232 port which simplified our lives immensely. What are you writing about the ps300?

Yes. It's in bloom when a vertex is centered in the inner circle. Maybe it goes from bloom to seed pods, the back to bloom. It is actually a rigid motion (translation) in hyperbolic space mapped to the plane.

Did you come here from the Fulldome group? This depicts one of the first fisheye images ever made. I'd like to see this on a dome!

@@stereosphere I did! I'd like to see it on a dome too! Fortunately I have one I can use-let me know next time you're in Salt Lake City!

Did you read the Dr Wood script? The picture is on display in the visitors center at Johns Hopkins university. I'd really like to do a really high res scan of the photograph, capturing every film grain. The print on display is most likely a contact print from the original film plate. I'd be very interested in seeing what sort of detail it contains. What is the best way to send you the frames?

I have not read the script, but I've had a growing personal interest in these kinds of techniques. Very cool.

Where is the comment?

On the Hamming page .

Actually, slicing on the diagonal is equivalent to an orthographic projection of the slice.