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A few highlights

Anaglyphs and stereoscopic pairs, Higher dim., Musical Geometries, How to make the musical geometries.

Anaglyphs, and stereoscopic pairs

You can show the picture as an anaglyph - this means that it springs into 3D when you view it using those red / blue 3D specs. Select this option from Picture | More Options. This can be useful for seeing the 3D shape of your flower. To buy glasses, see the NASA page Where to get your 3D glasses - any of the anaglyph ones are okay as there's an option to set the second colour to blue, cyan or green to match your glasses, also to set the background colour to black or white. You can also swap left and right in the anaglyph by making the eye separation a negative number.

There's also an option here to show coloured anaglyphs - have you seen one of those before :-). They work best with a black background. The picture above shows one of them. See the help for the red-colour radio button for details (hover mouse over it and press F1).

For some anaglyph pages made with Virtual flower see Anaglyph Garden (on-line)

Another option here is to show a stereoscopic pair. The help for that check box explains how to view them, so this is just to draw your attention to it.

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Higher dimensions

Now, I'd like to mention a special feature for those who like high dimension geometries, or are intrigued by them anyway :-). (Anyone else - just skip to the next section Intro to VRML).

You can show a couple of four dimensional shapes from Flowers Etc | Objects. These look good as wireframe anaglyphs.

Use the Single Object Tree button to make a virtual flower consisting of just your shape and no more.

They also nice in the trees - see the tesseract tree for an example.

For introduction to these shapes, see the tesseract page.

Use Caps Lock + drag to rotate the tesseract or simplex into the fourth space dimension. All the faces will seem to change shape as you do this - even the cubes that constitute its 3D faces - actually it's a matter of perspective, just as the square faces of a normal 3D cube look distorted in a 2D perspective view.

Techy note: as you turn your shape into the fourth dimension, you turn it around one of the axes of the three dimensional space the shape is projected into as well. A four dimensional planar rotation is a simultaneous rotation in two dimensions about a plane - rather than the rotation in two dimensions about a line that you get in 3D, which is how that can work.

Anyway, the upshot is that the figure changes shape as it turns. Maybe one could catch a glimpse of what a fourth space dimension could mean that way? ... Probably not, but, well you never know...

You can also use the drag and release method to set them spinning in the fourth space dimension.

The shape will change as the figure spins and the 3D pespective view on it changes.

You can also show the five and higher dimensional versions of these shapes by increasing the number for the dimension in this window. You can make a cube / hypercube in any number of dimensions, and the same also applies to the tetrahedron / simplex.

To turn the higher dimensional shapes into their respective dimensions, you use:

Caps Lock = dimension 4 as explained, Num Lock = dimension 5, Scroll Lock = dim. 6, Caps + Num = 7, Caps + Scroll = 8, Num + Scroll = 9, and Caps + Num + Scroll = 10. Each one gives you three rotations - in the plane common to the extra dimension, and each of the x, y and z directions in turn. You can also edit the rotations from Picture | Drawing Options, and you can scroll dimensions 4 to 6 using scroll bars.

You can also switch on hyper-perspective from this window. The idea there is to make a 3D perspective view in which the size of the 3D figure depends on its distance in the dimensions higher than 3. It's a commonly used perspective for the hypercube.

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Musical Geometries

This is a special option for users who also have my music fractals program Fractal Tune Smithy (FTS).

Intro, How to make the musical geometries, Audio formats to use, Midi clips and Cortona - special note


For an introduction to the idea of a musical geometry see the on-line page Musical Geometry. If you have installed FTS, you can also find a copy of this page in its install folder - default location C:\Program Files\Fractal Tune Smithy\mus_geom\musical_geometry.htm, with instructions on how to make all the midi clips for it in FTS.

Anyway, a quick summary - the idea is to start with a geometrcial shape such as an octahedron, and place a note at every vertex.

Then each edge plays a diad - the two note chord consisting of the two notes of the vertices it joins together.

Each face plays a chord consisting of notes for all its vertices. Most often one makes them with triangular faces - then every face plays a triad (three note chord).

Some of the models have solid tetrahedra - these play tetrads using the four notes at the four vertices.

The octony model has square faces, - this time each corner of the square plays a triad, and the complete square plays a tetrachord. You get all four constituent triads of the tetrad that way, just as you do if you use the more conventional tetrahedra for the tetrads - in fact a square with two diagonals is one possible way of projecting a tetrahedron into a plane.

The notes are usually chosen so that the triads are all pure and consonant just triads. As you move from one face to the next adjacent one, just as the faces share an edge, and so have two vertices in common, so the triads you play for them have two notes in common.

So the result is a visual geometry where the shape you see shows the connections between the triads you hear when you click on the faces - a wonderful kind of synthesis of geometry and music. One can think of it as a kind of musical abstract sculpture. Pieces get composed in them too - the innovative composer Kraig Grady has done a lot of work in these scales, and made some beautiful music in them.

I plan eventually to add music to Virtual Flower in some form. Meanwhile, you can't actually show these musical geometries in VF. However, you can make them in VF from the templates (with the help of Fractal Tune Smithy) and then show the resulting model in your VRML browser.

For details of the notation used in these models, and the tunings of the triads used to make it all work, see Exploring chords in the Wilson CPS sets (on line page) and to play in them yourself from p.c. or music keyboard, see the help for Fractal Tune Smithy. You could start at Help | FAQ | Music Making | How do I play in the Erv Wilson CPS Sets

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How to make the Musical Geometries

Start Fractal Tune Smithy (FTS) and use File | New, and select the voice you want to use for the clips from the Voice window. If you want to raise or lower the pitch of all the clips, use the Pitch window to do this.

To make sure that the notes will get played at the correct pitches in FTS, see Help | Overview | Test my midi player. Basically, you need to type #test into the musical seed box in FTS, then click the play button for the fractal tune - and if you hear repeated notes then FTS is able to play the pitch bends correctly on your equipment - and if not, see that help for more information about what you can do.

Now in Virtual Flower, and go to Output | Musical Geometry.

Choose what type of clip you want. See Audio formats to use to guide your choice.

Press Make Model and Clips. The midi clips get saved directly to disk in FTS, but with the audio clips you'll hear each one played in turn, and they get recorded as they are played. Note that short midi clips like this aren't recommended with the Cortona 4.0 VRML client (this is a bug that they aim to fix shortly).

For the audio clips, you need a full duplex sound card - one that can play and record at the same time, and you also need to select a suitable device from FTS | Bs | Record Control. Either choose Midi there, or "What U hear" or some such. Alternatively, save the clips in midi format, and use the Roland Sound Canvas software synth, as it has an option to render midi clips directly to waveform audio.

If you want to halt the recording, and start again, hold down Escape until it stops, or press the button to halt making the clips.

When FTS has fnished recording all the clips, press Show Model, and there it is, the 1 3 5 7 hexany.

Click on any of the spheres or numbers to hear the chords and notes.

To make another hexany, change the list of factors before you make it - e.g. 1 3 5 11 to make the 1 3 5 11 hexany. Make the new model in a new sub folder - change the folder to say, Hexany 1 3 5 11 - it's best if each model you make has its own folder

To make another type of CPS select the appropriate template from the drop list first.

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Audio formats to use

You can choose midi clips which is a special musicians format that only records note numbers, instrument numbers, and timings for playback. Files in this format are very small but the sounds heard are highly dependent on the user's setup - it is very popular for web pages for that reason. However, see Midi clips - special note.

The others formats record the actual sound played: waveform audio (*.wav), mp3s, Sun Au (suitable for java applets like Blaxxun 3D) or finally, the option to choose the audio format in FTS.

To set the bit-rate for the mp3s in FTS go to Bs | Record to File Options, choose mp3 from the drop list, and a field to set the bit-rate will appear. 128 here is high quality. You can go down to say 32 or even 16 for highly compressed notes and chords.

You need to set FTS up so that it can record in mp3, Sun Au and other formats using a couple of free helper apps - see FTS | Help | FAQ | General | How do I record and open files in Waveform audio formats (Wav, mp3s, Sun au, etc)?

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Midi clips and Cortona - special note

The midi clips aren't recommended with the Cortona 4.0, as it has a bug that prevents it playing these short midi clips properly apparently related to Direct Sound (it also misses some notes in longer clips too). They have confirmed that it is a bug and will fix it. Alas this means that you can't really use them in web pages yet, at least not without special notes and warnings for the visitors to the page, as the Cortona is probably the most frequently used method of viewing web pages in VRML.

Cortona is also very slow at loading models which have many small clips such as some of these,and in fact your computer may stop responding when it does so - it's best not to make the dekanies for Cortona, even in the audio formats. Sorry about that! Again they are looking into this.

You can make the hexany in Cortona using audio clips / mp3s. You can make any of the models if you are using the old Cosmo Player, or an earlier version of Cortona prior to version 4.0. You can also show the models using Blaxxun, if you make the clips in the java Au format.

However, the Cortona can play mp3s! (That is a rare feature for a VRML viewer). So as a work around for models to upload, one can record all the clips as mp3s.

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