Property of The Geometry Center. All rights reserved. \documentstyle[moviescript,12pt]{article} \newenvironment{pupil}{\bgroup\sf}{\egroup} \begin{document} \part*{Mad About Mirrors} Mad About Mirrors - 7/18/95. %Summer 95 project Anna Gardberg, The Geometry Center. Rights Reserved. \section{Title Sequence} \begin{scene} \subscene \\ Title: "Mad About Mirrors". Hold on title at angle for 2 seconds \timing{hold}{2} \\ \subscene \\ The title flies around in a large circle, eventually centering. \timing{swirl and center}{8} \timing{hold}{3} \\ \subscene \\ Fade to empty plane. \timing{fade to plane}{1} \\ \end{scene} \section{Playing With One Mirror} \centerline{Triangle and Mirror Arrive}\smallskip \begin{scene} \subscene For today's introduction to mirrors and symmetry, we need a demonstrator. Luckily, a famous Flatlander has volunteered. We also need a mirror. \\ Hold on empty plane; the triangle arrives. \timing{empty plane}{3} \timing{arrival}{4} \timing{hold}{0.5} timing{zoom}{1} \\ \subscene Hi, my name is Triangle. \\ Hold on triangle. \timing{hold}{3} \\ \subscene \\ First mirror arrives. It is not completely reflective, so a faint pink color can be seen. \timing{arrival}{2} \\ \end{scene} \centerline{Mirror Tilts}\smallskip \begin{scene} \subscene Watch what happens as the mirror tilts backward and forward. \\ Hold on newly arrived mirror. \timing{narration}{4} \\ \subscene \\ Mirror tilts backward. \timing{tilt}{3} \\ \subscene My reflection tilts when the mirror does, says T. \\ \timing{hold}{2} \\ \subscene \\ Mirror tilts forward, scene holds. \timing{tilt}{6} \timing{hold}{2} \\ \subscene \\ Mirror returns to vertical, perpendicular to plane. \timing{tilt}{3} \\ \end{scene} \section{Playing With Two Mirrors} \centerline{Second Mirror Arrives}\smallskip \begin{scene} \subscene When we add another mirror, things get considerably more interesting. \\ Hold on upright mirror. \timing{narration}{4} \\ \subscene \\ Camera pulls to the side. Hold on side view. \timing{Camera motion}{3} \timing{hold}{1} \\ \subscene \\ Second mirror descends from above. It's faintly blue in color. Appropriate sound effect. \timing{arrival}{4} \\ \end{scene} \centerline{Tilting Corridor}\smallskip \begin{scene} \subscene Again, we can tilt the mirror backward and forward, but this time, we see much more. \\ Hold on side view. \timing{narration}{5} \\ \subscene \\ Camera moves to corridor to face the first mirror, then the action pauses. \timing{camera motion}{3} \timing{pause}{1.5} \\ \subscene \\ The first mirror tilts backward slightly, and we see the ``barbershop corridor'' seem to curve downward. The action pauses, so the viewer can see what's happened. Perhaps a sound that decreases in pitch should go here. \timing{tilt}{2} \timing{pause}{1} \\ \subscene \\ The mirror reverses direction, ending up tilting forward. Perhaps a sound increasing in pitch, then decreasing. The action pauses. \timing{tilt}{4} \timing{pause}{1} \\ \subscene \\ The mirror returns to vertical. Pitch increasing sound. \timing{motion}{2} \\ \end{scene} \centerline{Dihedral Symmetry --- $90^{\circ}$}\smallskip \begin{scene} \subscene By lining up two mirrors edge to edge, we can see what is called dihedral symmetry. \\ Hold on the corridor. \timing{narration}{6} \\ \subscene \\ Camera moves to a diagonal view, and the action pauses for a moment. \timing{motion}{2} \timing{hold}{0.5} \\ \subscene \\ Blue mirror moves to align with pink mirror at ninety degree angle. Text ``$90^{\circ}$'' appears in view, and the scene holds. \timing{motion}{2} \timing{text and hold}{2} \\ \subscene There are four of me, and two are mirror reversed, says T. What happens when the angle changes? \\ Text disappears, camera moves closer to see the interior, and stays there for a moment. \timing{motion}{3} \timing{hold}{2} \\ \end{scene} \centerline{Dihedral Symmetry --- $45^{\circ}$}\smallskip \begin{scene} \subscene \\ Camera retreats again, and action briefly pauses. \timing{camera}{2} \timing{pause}{0.5} \\ \subscene \\ Blue mirror moves to align with pink mirror at forty-five degree angle. Text ``$45^{\circ}$'' appears in view, and the scene holds. \timing{motion}{2} \timing{text and hold}{2} \\ \subscene Now there are eight of me, and four of them are backwards. \\ Text disappears, camera moves closer to see the interior. When the triangle has completed its motion, the triangle comes into view, if it's not already. This view pauses. \timing{camera motion}{2} %\timing{triangle moves}{2} \timing{hold}{2} \\ \end{scene} \centerline{Dihedral Symmetry --- $60^{\circ}$}\smallskip \begin{scene} \subscene \\ Camera moves back, and there is a brief pause. \timing{camera}{2} \timing{hold}{0.5} \\ \subscene \\ The blue mirror moves to a sixty degree angle, and the text ``$60^{\circ}$'' appears. There is a pause. \timing{motion}{2} \timing{text and hold}{2} \\ \subscene \\ The text disappears, the camera moves in, and there is a brief pause before narration of the next act. \timing{motion}{2} \timing{pause}{0.5} \\ \end{scene} \section{Three Vertical Mirrors} \centerline{Third Mirror Arrives}\smallskip \begin{scene} \subscene When we add a third mirror, we can see reflections extending across the entire plane. \\ Camera holds on sixty-degree kaleidoscope. \timing{narration}{6} \\ \subscene \\ Camera pulls away from mirrors, then turns $180^{\circ}$; the rotation may involve moving the interest. \timing{translation}{2} \timing{rotation}{2} \\ \subscene \\ The third mirror arrives. It is faintly yellow or green. There is now a 60-60-60 triangle of mirrors. Angle labels appear at the corners, and this view is paused. \timing{arrival}{2} \timing{text and hold}{4} \\ \end{scene} \centerline{The $60^{\circ}$--$60^{\circ}$--$60^{\circ}$ Triangle of Mirrors}\smallskip \begin{scene} \subscene \\ The camera moves into the kaleidoscope, and there is a pause. The triangle may have to move. \timing{camera}{2} \timing{hold}{1} \\ \subscene Wow! My images go on forever, exclaims T. \\ The camera pans through $360^{\circ}$, then briefly pauses. \timing{pan}{10} \timing{hold}{1} \\ \end{scene} \centerline{$45^{\circ}$--$45^{\circ}$--$90^{\circ}$ Triangle of Mirrors}\smallskip \begin{scene} \subscene We can do this for different mirror arrangements, as well. \\ Camera pulls away again. Hold on view for duration of narration. \timing{camera}{2} \timing{narration}{4} \\ \subscene \\ Mirrors transform to $45^{\circ}$--$45^{\circ}$--$90^{\circ}$ triangle; text appears, labelling angles, and there is a pause. \timing{transformation}{2} \timing{text and hold}{4} \\ \subscene \\ The text disappears, and the camera moves into the kaledioscope. The triangle may have to move. \timing{camera motion}{2} %\timing{triangle motion}{1} \timing{hold}{0.5} \\ \subscene \\ The camera pans through $360^{\circ}$, then briefly pauses. \timing{pan}{10} \timing{pause}{1} \\ \end{scene} \section{Polyhedral Kaleidoscopes} \centerline{Transition}\smallskip \begin{scene} \subscene You've just seen how kaleidoscopes work. They're made of mirrors that reflect the same image many times. You've also seen that tilting a mirror causes the image in it to tilt as well. Now, watch what happens when these two ideas are combined. \\ Continue to hold on the inside of the $45^{\circ}$--$45^{\circ}$--$90^{\circ}$ kaleidoscope. The image should go as far as the eye can see, so the reflectivity should be turned way up. \timing{Narration}{15} \\ \subscene \\ The camera moves up, and perhaps slightly sideways. \timing{translation}{1.5} \\ \subscene \\ The mirrors transform to cubic symmetry \timing{trnsformation}{2.5} \\ \end{scene} \centerline{Cubic Kaleidoscope}\smallskip \begin{scene} \subscene The kaleidoscope's mirrors are arranged along the planes of symmetry of a cube. The chamber itself is 1/48 of a cube. \\ Fade to identical scene, but with kaleidoscope mirrors clipped for a neater look. [Note -- no hole in the bottom] There is a brief pause. \timing{fade}{1} \timing{narrate}{8} \\ \subscene Can you see a three dimensional figure in the reflections? \\ The kaleidoscope translates downward to pierce the plane in such a way that we see triangle man on the faces of a cube. The camera moves to get the best view of the interior image. Pause, to let the cube be recognized, and to narrate. \timing{translation}{1} \timing{camera motion}{1.5} \timing{narration and hold}{4} \\ \subscene The same arrangement of mirrors can show several different shapes. \\ Hold on cube view. \timing{narration}{4} \\ \subscene \\ Rotate the plane with the triangle, or rotate the kaleidoscope itself, to show the ``cube'' become an octahedron. Pause. \timing{motion}{1.5} \timing{hold}{2} \\ \end{scene} %\centerline{Icosahedral Kaleidoscope}\smallskip %\begin{scene} %\subscene %Different arrangements of mirrors give even more shapes. %\\ %Hold on view of octahedron. %\timing{narration}{4} %\\ %\subscene %\\ %Camera moves away, kaleidoscope clears the plane. View is such that the %upcoming trransformation will be easily noticed. %\timing{camera moves}{2} %\timing{kaleidoscope moves}{2} %\\ %\subscene %\\ %Fade to icosahedral kaleidoscope. %\timing{fade}{1} %\\ %\subscene %\\ %Kaleidoscope pierces plane. Camera moves in for best view of an image of %a dodecahedron. Pause. %\timing{Kaleidoscope motion}{2} %\timing{camera motion}{2} %\timing{hold}{3} %\\ %\subscene %\\ %Rotation of kaleidoscope or plane to show different shapes, ending on %icosahedron. Pause. %\timing{rotation}{4} %\timing{hold}{3} %\\ %\end{scene} \centerline{Tetrahedral Kaleidoscope}\smallskip \begin{scene} \subscene Different arrangements of mirrors give even more shapes. \\ Hold on view of octahedron. \timing{narration}{4} \\ \subscene \\ Camera retreats. Kaleidoscope retreats. Brief Pause \timing{Camera}{2} \timing{Kaleidoscope}{2} \timing{hold}{0.5} \\ \subscene \\ Fade or transform to tetrahedral kaleidoscope. Kaleidoscope pierces plane and camera moves in to show image of tetrahedron. \timing{transform}{4} %\timing{fade}{1} \timing{hold}{0.5} \timing{kaleidoscope motion}{2} \timing{camera motion}{2} \timing{hold}{1} \\ \subscene \\ Rotation of something to show various shapes. End on tetrahedron, not too large. \timing{rotation}{4} \timing{hold}{4} \\ \end{scene} \section{Four Mirrors and a Tiling} \centerline{Tiling space with tetrahedral kaleidoscope}\smallskip \begin{scene} \subscene You can recreate the symmetries that you've seen here so far with a few mirrors or with a computer program such as Jeff Weeks' Kaleidotile. Here, however, is an arrangement that might give you some trouble if you were to try it in real life. \\ Music swells (A fragment of Bach's Toccata \& Fugue in D minor would be nice). Hold on tetrahedral kaleidoscope. \timing{narration}{10} \\ \subscene \\ Music continues. Camera moves to face opening. It is within the confines of the kaleidoscope. A fourth mirror comes into view and hangs above for a moment. \timing{camera}{1} \timing{mirror arrives}{2} \timing{hold}{2} \\ \subscene \\ At a time appropriate to some climactic music, the mirror swoops in to complete the tiling of space. Pan majestically around, until the music ends, or gets to a good place. Tentatively 15 seconds. Fade out during pan. \timing{swoop}{1.5} \timing{pan}{15} \timing{fade}{2} \\ \subscene \\ Cut to credits. Stuart, Chaim, music \& sound folks, title, Geometry Center page, NSF. Credits as long as necessary. Approx. 10 sec. \timing{credits}{10} \\ \end{scene} \end{document}