Yahoo Tuning Groups Ultimate Backup tuning FW: Formula/arrow temperaments, and 6 dimensional/octophonic Mandelbrot noise.

Forwarding another message from Sarn Ursell:

>Date: Sun, 3 Jan 1999 08:59:08 +1300
>From: Sarn Richard Ursell <thcdelta@pop.ihug.co.nz>
>Subject: Formula/arrow temperaments, and 6 dimensional/octophonic
> Mandelbrot noise.
>
>
>FORMULA ARROW TEMPERAMENTS, OCTOPHONIC MANDELBROT NOISE:
>
>Hello fellow retuners!
>
>I am thinking of using the "Mandelbrot set" in a 19ET AI composition.
>
>I want to mak what I call "Mandelbrot noise".
>
>What type of software do you think I should use?
>I need something that can do imaginary and complex numbers and also additive
>sytnthesis, changing over time continuously.
>This is very like "granular synthesis".
>
>Something with a fine color resolution, and a fine sound resolotion.
>Mabey Mandelbrot noise would sound like chaotic brownian noise changing over
>time.
>
>The fractint program isn't what I thought it would be-it doosen't do powers
>of powers of powers for complex numbers.
>
>I was thinking of doing an "16ophonic" (or 6D-quadruple steryocube) AI
>Mandelbrot noise composition in 19ET/19 Quiggle/19 revers quiggle
>temperament- each temperament division in 19ET a timbre based on a
>Mandelbrot set of the form z-->z^((2^(1/19))^n).
>
>This would probably run for 70 seconds, with that amount of information.
>
>Get a computer to emulate a recording in 16 points in 3D space, or 16
>pointsin 4D space.
>How could I make it so people with a 16 speaker system would hear
>16ophonics, people with an 8 speaker system would hear octophonic, people
>with a quadrophonic system would hear quadrophonic, people with a steryo
>system would hear steryo?
>
>I feel that part of the composition on any CD should be its position in the
>steryo field-all part of the artistic package.
>I would also like to:
>
>1.Graph a 3 dimensional version of the Mandelbrot set.
>By this, I DO NOT mean, a standard Mandelbrot set with the colors raised in
>a surface, but an actual Mandelbrot solid, embedded in 3 space.
>The 3rd dimension could be the Logarithm of a negative number, or what I
>term an "L" number, a real, an imaginary, or a hypercomplex number.
>It would be good to define a view point of the 3D Mandelbrot with some of
>its outside shell shaved away, or with a reverse color spectrum , fly around
>it and into it, rotate it by the xy, xz, yz axis, take 2 dimensional slices
>of it.
>I would also like the capabilitys to graph different mathematical formulae,
>Could you calculate the curve length, magnitude and slope of the iterated
>complex formula, and also the surface area of the 3D Mandelbrot set solids
>plane, (ie.the surface made by slices of the Mandelbrot Set solid, with
>color=height).
>I would like to be able to use different colored light sources/shadows on the
>Mandelbrot set, treat it as a mirror, and make it transparent/opaque.
>
>
>2.Treat the Mandelbrot Set as a matrix, with position on complex plane= rows
>and columns, color =matrix value, and multitply it, and geometrically
>average it, add and average the diagnols from each square, treat the matrix
>as power of power of powers in a spiral fashion and average it using
>...(x^(x^(x^)))'s equivalent root.
>Iterate the values of these numbers in the complex plane ect...
>We could let each color value stand for a binary matrix, and then alter it,
>or use imaginary, negative and real numbers to be added.
>
>3.Overlayer 2 different Mandelbrot set formulae, say z->z^2+c and
>z->z^3-(1/c) via 10000 frames of time, and blend/average the pixels color
>with respect to time.
>This could be done for ipeg images of cartoons, plants at various stages of
>growth, waveforms at various stages of time.
>
>4.Handle really big numbers and their roots, and also operater like "power
>of power of powers of powers...) and its equivalent root.
>Ie.(....(x^(x^(^x(x^x))))=x&c, and ((((x^x)^x)^x)^x)....=x&.c
>Is there a specific notation for these?
>
>5.Is there a software package that can handle my "arrow notation":
>x+y=x(1 up arrow)y,
>x*y=x(2 up arrow)y,
>x^y=x(3 up arrow)y,
>x&y=x(4 up arrow)y....ect...
>(What would negative, imaginary, complex, L arrows be?2.5 arrows?Equivalent
>root values?).
>
>6.Does I need a software package that has the ability to animate, and change
>color in 4D and 5D, do calculus, quartonians, octonians ect?
>
>7.Create a fractal acoustically modeled instrument, like a "tree branch
>trumpet" , or an instrument produceing FFT fractal noise.(What about making
>an acoustically modeled intrument from Mandelbrot Noise?).
>
>8.Do fractal cellular automa, and ants on the Mandelbrot set (Cellular
>automa-->computer scans each sqares sourronding squares colors, giving each
>color a score and totaling it.
>Depending on the score, it subtracts a certain value from the central
>squares score, thus changing its color.
>Ants--->Computer scans each square one at a time.
>Depending on their color, the square heads 90 degrees anti-clockwise one
>square, or 90 degrees clock wise one square.
>Depending on the square it lands on, it will change its direction.
>In addition to this, it changes the squares color it has left from.
>If two or more squares land in the same place, the square effects all their
>movement.
>We could even graph color square landed on vs color square changes to vs
>color that moving square changes to.
>
>9.Acoustically model the Mandelbrot set.(This would be really interesting).
>
>11.Define a number that is the "Quiggles equiivalent root" of -1.
>IS there such a number?What about quiggle roots of i, -i, L, -L, iL, -iL.
>
>10.Define logs or L numbers eg log(10L)=L(2), log(10(2L))=L(3), and also
>(-1)quiggle roots as "Q" numbers ect....
>
>13.Define a class of numbers with different propoerty for addition,
>multiplication, powers, quiggles ect....
>
>11.I realise that you can join a line of existing photographs into a strip
>to make a panoramic image.
>
>12.Panoramic images have been done before.
>
>13.Use the Mandelbrot set as a time stretch/up sample jelly (jello to you
>Americans!) algorithm.
>Real=time, imaginary=time stretch/compress, color=up sample/down sample.
>We could use combinations of the above axis, imaginry=time, color time
>stretch/compress, color=up/down sample.
>
>Has this ever been done for a full sphere, in all x, y, z axis?
>It would be difficult to control by hand, of course!
>
>Microphones are, by default, quasi-sphereical.
>
>Obviously, the smaller the photographs (down to pixel size), the less
>distorted the end result will be.
>
>Its impossible to map/squash a hollow sphere down onto a flat surface
>without distortion.
>We could do it by mathematical manipulation, however.
>What is the algortihm used to do this?
>
>Failing this, could we take 6 square photographs, and alter them
>mathematically by averageing/blending formulae to generate squares into -->
>spheres?
>
>What about "sphereical real time", looking in on an image from all
>directions? photography, also known as "time slice" photography.
>I've seen it done as a strip, but not a movie.
>
>(This would probably be impossible, as the other cameras would get caught in
>a video-feedback loop, unless they were viewed from a great distance.
>Perhaps you could use 8 video camers with a suitably wide view field/cone,
>and blend the images by computer).
>
>The same would apply to realtime panoramic photography, unless the
>photographer was concealed, between takes.
>
>What would a realtime sphereical panoramic, and/or time-slice viedolook like.
>Using bigger focal lengths, zoom lenses, we could magnify the images also,
>without loss of resolution.
>
>What about taking a time slice video of a head from all directions,
>ie.looking in from a sphere, and morphing squares from the frames into an
>"unraveled head" in realtime, or steptime video.
>We could pull faces, turn around ect.
>Use a different color filter for each image.
>We could have an inverse panoramic image of the 3D Mandelbrot set solid's
>surface, flattened on a plane, being magnified.
>
>13.What would the effect be of taking slices of a moving picture footage,
>and averageing the pixels colors (0-1000 on a ROYGBIV spectrum, or RGB color
>scale) via time (eg (pc(1)+pc(2))/t(2)-t(1)=pc(3) at t(3), where pc=pixel
>color value, t=time.
>We could take the geometrical and harmonic averages, the slopes of the color
>gradually changing via time?
>
>This would be interesting when combined with panoramic images or "time
>slice" in 3D.
>
>What about a combination of the above ideas in steryoscopic vision?
>
>A mathematical formula to alter the color of the graph, eg pc(n)=sin(pc)n.
>
>14.What fasinates me is the relationship between graphical effects and
>acoustic effects.
>Could we harmonically analyse a sample for its relevance to the temperament
>were playing in, and give it a "beauty score" for that temperament?
>
>Finally, if you want to talk about my "arrow synthesis", and mathematical
>formula snake temperaments, let me know!
>
>Any ideas?
>I look foward to hearing from you,
>Food for thought,
>
>Happy new year,
>
>Sarn Ursell.
>
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| Mark Nowitzky |
| email: nowitzky@alum.mit.edu AIM: Nowitzky |
| www: http://www.pacificnet.net/~nowitzky |
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FW: Formula/arrow temperaments, and 6 dimensional/octophonic Mandelbrot noise.

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