The Umpteenth Dimension A world of reflections.

 Imagine being inside a sphere (or torus) that is perfectly reflecting - just you and a light source. What would it look like? With the aid of the graphical raytracing program POVRay I try to answer that question. Below are several animations and still images where I explore such impossible worlds. Thanks to Ioannis Galidakis for the inspiration that led to this work.

 The Observer First some comments about the 'observer'. I'm not a good artist, so I didn't try to make a virtual person to be reflected. Instead I went with the simple and just used a simple marble sphere and placed the camera on it, right on its nose, so-to-speak. Here is a picture of 'you' so you know what is being reflected. The camera is placed right in the center where you see the white spot reflection of the light source. Trust me, you probably won't recognise yourself by your reflection most of the time anyway. Click on the image for a 1600x1200 version. (832,392 bytes)

 The Animations & Still Images The animations are 12 second AVI's in mpeg4 running at 10 fps with a 320x240 frame size. The high res images are 1600x1200 minimally compressed jpg's.

 The Floor For each, animation or still, there are two versions. One is the world with just you and the light source. The other adds a red and green checkered floor. The size of the checker squares is 1 unit. Each animation or image of the pair is the same except for having or not having the floor. The purpose of the floor is to help you get a feel for the movement going on in the animation. In some of the scenarios it's difficult to get a feel for your motion through the scene, but having the fixed floor to look at as a reference keeps your mind from freaking out too much.

 Coordinate System Oh, a note about the coordinate system. In POVRay we use the left-hand rule. That is, if you hold up your left hand and make an 'L' with your thumb and index finger, then stick you middle finger half way up so it's pointing away from you, then you are showing the three positive directions. In other words, positive x is to the right, positive y is up, and positive z is away from you into the monitor. The center of the universe in is at <0, 0, 0>.

The Sphereverse

In the Sphereverse, the universe is a sphere 40 units in diameter. When there is a floor present, the floor is 2 units down from center.

Click on the image to see the large image. Click on the link to get the animation.

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In this animation you are sitting back 10 units from the center of the sphere. The light source is translating from left to right centered on the x axis. You are not moving, only the light. All the concentric rings are caused by your multiple reflections in the sphere.

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This animation is the same as the above except now you are sitting 2 units higher than before. That is, you are two units above the plane that the light is traveling in. You are looking straight forward and not down towards the light.

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This time were back to our original height of 0, but this time the light is 2 units higher. It's travelling form left to right just like in the first two animations.

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This animation has the light sitting centered at <0, 0, 0> and you are moving. You start back at the sphere's edge at -20 units and move straight toward the light, through it, and on to the other side at +20 units. Notice how the concentric rings change and get thicker as you approach the center of the Sphereverse. This is because you are approaching the focus of the reflection and the reflection is a focused image of yourself! After you pass through the light source the rings start getting thinner again. Finally, as you approach the far side of the Sphereverse you begin to see a refleciton of yourself, which is the dark circle which finally fills the view at the end.

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Now we take the same journey as above except you are 2 units above the light and looking straight ahead. This looks much the same as before except the concentric rings are not centered on each other.

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In this animation the light source is at the center of the sphere and you and position back 10 units. You don't move, but simply rotate to look all around you.

 The Torusverse The Torusverse is life inside a perfectly reflecting torus. 'Torus' is just a fancy word for the shape of a donut. At this time I have not yet done the animations for the Torusverse. But you can expect similar travels in the Torusverse