I've currently moved over to blogging at http://mathcraft.wonderhowto.com/

Here I will be posting about 4 times per week and will have a project every week with more in depth information and a how to component and templates. There will also be a user forum for people to submit pictures and ideas.

Thanks! I hope to see you there!

Some interesting Photos

This post is going to be a bunch of random pictures that I think demonstrate something interesting or cool. The first few are just some close up nature still life shots. There are some high speed water pictures, some pictures playing with lights, a picture that shows the earth spinning, an ultra closeup of an eye, and a couple that show an interesting idea of changing zoom while taking a long exposure. I've commented on most of the individual pictures with the technique I was using/idea I was going for. All of the originals are 4000 x 3000 but blogger only allows 1600 x 1200. I still recommend clicking on the picture to see it at this size.



I really liked taking pictures of the lizard in the next 3 pictures. He was trying to hide so he was staying as still as possible. The camera is less than a foot away from him. Only the last picture is a crop.

Here it has an eye wide open



Here you can see a little bit of the front of its snout.



Click on the picture below to see the crazy details. This is cropped to actual pixels from the first picture of the lizard.



Close up of water drops on a leaf. I really like the shapes that water drops form depending on what surface they are on. I also really like the reflections. I need to play around with arranging water drops sometime.



With a shutter speed of 1/4000 of a second, you can get some pretty cool pictures of water though due to all the motion it is really hard to focus on. I took a bunch of pictures of water coming out of a spigot. This one turned out pretty cool.



Another of the water shots. In this one it is coming out at the camera.



This was shot at late twilight with a tripod. I started out zoomed in a 10x and then with a long exposure zoom out to be completely wide. This would give you straight lines. In order to get the smooth curve I rotated the tripod head while zooming out.



The camera was on a stationary tripod in the picture below. (The camera was not moving with respect to the ground at all) At 10x zoom with a 60 second exposure you can really see how the earth is spinning. I've really boosted this picture beyond where it should go in order to see more streaks. In the original you can see the colors of the different stars. I need to shoot in raw so that I can keep more information and this even after boosting would be much cleaner. I'm really tempted to see whether I can look at the distribution of path lengths in order to find what the center of rotation is and calculate the rotation rate of the earth. It will be like the old days tracking particles in Wolfgang Losert's Lab!



Long exposure taken at 10x zoom of city lights while moving the camera up and down multiple times to get so many streaks.


This is a 1 second exposure using a tripod where I start out zoomed in 10x and then zoom out completely wide. This causes perspective lines to appear where there are bright objects being photographed. This works really well on the guitar. I need to play with this in a cooler location than my classroom!




My brother's eyeball. This is not a crop. I used a cheap macro adapter and zoomed in at 10x. His eye was probably about 2 inches away from the lens. The depth of field is crazy shallow. I need to take this picture in daylight instead of indoors and I need to make sure my white balance settings are right! Still pretty cool, look at the detail on the very center of the eye.

Aerial Panoramas 1

If the lighting is good and the window isn't too scratched up, you can take pretty good pictures out of a plane window. I'm sure someone else has done this but I've never seen images out the windows of airplanes stitched into panoramas. Here are a few that I've taken. I'll probably post up most of the others tomorrow. While planes are traveling at a few hundred mph, the distances to objects are enough that you can still take your time when snapping the pictures to stitch together. The exception to that rule is right around takeoff or landing. One of the pictures here is flying over Sacramento around sunrise and you can see that the panorama is distorted. I waited too long between pictures...

Just click on the pictures to see slightly larger versions.






















Panoramas again.

Here are some old panoramas. I decided I would post up some that maybe aren't the prettiest, but that involve something interesting. The first is one of the first panoramas I ever took. It was stitched together by hand instead of using an automated program. I think it is a very pretty picture of New Hampshire in the fall. In the next two pictures you can see how to take panoramas with portraits. This is one real advantage of stitching photos together. If you take all of the panorama pictures and then have someone take a picture from the same spot that you are in...you can be in the panorama. The next is an image of the Golden Gate Bridge from an unusual perspective. I really need to go back and take this correctly to fill in the gaps. The following image is Chicago taken from a moving ferris wheel on Navy Pier. Taking panoramas from moving objects actually works really well. In another post I'm going to post up pictures taken from moving cars and even airplanes. Next is vertical panorama of the inside of the Chicago Macys (Old Marshal Fields). I think that vertical panoramas are really underutilized. The last two shots are the least interesting of the bunch in my opinion. One is a picture of a topiary garden in Maryland and finally just for fun I thought I would post up my panorama of the lone cyprus (the most photographed tree in the world)
















Sierpinski Tetrahedron

The Sierpinski Tetrahedron is an object with a fractal dimension of 2. If you keep iterating the object (removing the middle shape out of the remaining tetrahedra) then the volume of the object goes to zero while the surface area remains the same. In some sense it is a 2 dimensional object composed of 3 dimensional objects. In fact if you look at the Sierpinski Tetrahedron in one of 4 special ways it actually looks like part of a plane (a sheet of paper.) For a while I've wanted to use this to put two different pictures on one that you can only see when you look at it from a certain perspective. When you are done looking at the pictures you can click on this link to see my inspiration. My version is only the first iteration and I built it to make sure that I understood how to make it. Due to the 3 d nature of the shape you must distort the picture quite a bit in order to have it look right, and it was a bit of a puzzle to figure out exactly where each piece went. Eventually I want to make a version with 64 pieces (iteration 3) instead of 4.

I decided to use a picture of a moonrise on one side and an earthrise on the other to have something where you are seeing something from exact opposite perspectives. The video at the end is a quick mockup of how I could have it set up on a spinning stand.

Earthrise!





Moonrise!







More new camera pics

Day 2: I spent a couple of minutes shooting some more pictures. For the first few I even had a hot model pose for me! After that are some pictures of some flowers. The flowers are Alyssum. (Thanks Asa for the information).

Liz:








Flowers:










Elvis:




Oak at night:

New Camera

I finally got an Digital SLR style camera. All I have used for the last 4 and a half years is an ultracompact. Now I have no excuses for my bad photography. I ended up buying a Panasonic GH1 since my brother had one and it would be nice to exchange lenses, plus the standard lens it comes with is pretty phenomenal. It is the same camera we used for the Doritos Superbowl Contest to make this video. Here are the first few pictures. Click on the pics for 1600 x 1200 resolution. (The originals were 4000 x 3000)

Jay (Western Scrub Jay according to Liz):




Leaves:



Elvis:



Nuts!:


Playing with Lights:


Hyperboloid

This continues on the idea of making curved shapes out of straight lines (see the previous hyperbola posts here and here). I made an sculpture using bamboo skewers and rubber bands. The object I made is called a hyperboloid which is the shape that you would get if you took a hyperbola and rotated it around a fixed axis. If built correctly, it would be curved even though it is composed entirely of straight lines. Mine is actually bent because I have not spaced to rubberbands correctly. The skewers are actually bent in a way that would make it so it would curve inward instead of outward so if I were to take the time to fix it, it would actually bend more.

One cool thing about building the shape using rubberbands is that the joints where the skewers meet are free to rotate meaning that you can expand and contract the object. In many of the pictures I have expanded it out using a cog from my orrery project.

I learned how to make this object here and it is not hard to do, but it does take a while.

















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