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.

>

+------------------------------------------------------+

| Mark Nowitzky |

| email: nowitzky@alum.mit.edu AIM: Nowitzky |

| www: http://www.pacificnet.net/~nowitzky |

| "If you haven't visited Mark Nowitzky's home |

| page recently, you haven't missed much..." |

+------------------------------------------------------+

Message written at 6 Jan 1999 10:43:22 +0000

CC: thcdelta@pop.ihug.co.nz

In-reply-to: <2.2.16.19990103155130.3c8770fe@pacificnet.net> (message from

Mark Nowitzky on Sun, 3 Jan 1999 15:55:05 -0800 (PST))

References: <2.2.16.19990103155130.3c8770fe@pacificnet.net>

>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?

Yes, it is a superpower, 4th in the series of operations in

Ackermann's function, and I have seen it notated as X^^Y

==John ffitch