# Is this the PHI of 12 tone music? Equal tempered semi-tone multiplier

Posted by tomachi on July 25th, 2017 filed in ScienceComment now »

Take any positive number, multiply it by this number twelve times, then divide by 2. **Same number you started with in theory. **This should be what you multiply a tone frequency like concert pitch 440 hertz to get A# as 466.16 hertz.

So I finally found a use for Wolfram Alpha! I was able to use it factor or solve the quadratic equation:

To find the value of X when A > 0, and also when A*X*X*X*X*X*X*X*X*X*X*X*X = A*2

The solution is that X = 2^1/12 (two to the power of 1/12). Which is roughly **1.05946309** or more precisely:

# Neocortex – 3 minute 3d mandelbrot fractal animation

Posted by tomachi on July 11th, 2017 filed in VisualsComments Off on Neocortex – 3 minute 3d mandelbrot fractal animation

Youtube Low Res Test Render: https://youtu.be/QG-bJeH5D5Y

Mandelbulb3D Source file: Stripey Beast v14

Feed that into Mandelbulb3D and render at 1920 x 1080 with anti-alias 2. Output format jpeg. Like this:

# BREAKING NEWS: Cliff collapse in Kohimarama

Posted by tomachi on April 4th, 2017 filed in NewsComments Off on BREAKING NEWS: Cliff collapse in Kohimarama

Cliff collapse in Kohimarama ~~persons unaccounted for~~ (they safe now)

#Breaking #Auckland #landslide #missionbay #kohimarama

It was not before 8:40pm. But after 8pm maybe. I can still feel the odd after-shock I reckon. I’m located in Comins Crescent but have no idea till the morning where this landslide is located. My theory: the Nihil Reserve earthworks nearby. Hopefully I’m still here in the morning. If not…. well it has been a sweet sweet life. Can die happy. Ready to be swallowed up, but hey I might go for a midnight walk in the rain…

# Sine Wave Zion – Additive Colour Demo in Shadertoy

Posted by tomachi on March 17th, 2017 filed in VisualsComments Off on Sine Wave Zion – Additive Colour Demo in Shadertoy

Chilin – my African friend asked me if I could make a shader to visualise a sound or sine wave with harmonics included, so I wrote this WebGL shadertoy:

In the end, I didn’t quite get there but this shader makes a nice illustration of the theory of additive colours, as various offsets of the sine waves are given their own channel: Red for the main frequency, Green for the second harmonic or octave, and Blue for the third harmonic.

**Features:** sine waves, pi, mouse input to alter parameters, interference patterns

## Highlights of the code

This is just a normalised sine function of time multiplied by the pixel co-ordinates being rendered.

vec2 S; // speed of fundamental

S.x = (xy.x + xy.y)*(xy.x – xy.y)*0.5; // “velocity potential” a square of the pixel distance so it gets big quick

S.x -= iGlobalTime *timespeed; // animate stream

vec2 sxy = sin(3.14159 * S * 1.0 ); // its a sine wave of time and pi

### The Full Code

// Concept: an animation of wave harmonics // show 1st, 2nd, 3rd order harmonics somehow float divs = 2.2; void mainImage( out vec4 fragColor, in vec2 fragCoord ) { vec4 m = iMouse; if ( m.x == 0. && m.y == 0.) { m.x = iResolution.x / 2.; m.y = iResolution.y / 2.; } float dist = m.x - ( iResolution.x / 2.0 ); // centererd float speed = 0.0009; // 0.9 camera movement to plane float timespeed = 0.1 ; // 0.1 wave movement on the ribbons // MOUSE: multiple by my or mx to get value between 1 and 2 float my = float( (m.y + iResolution.y ) / iResolution.y ); float mx = float( (m.x + iResolution.y ) / iResolution.x ); float t = 8.0 - speed ; // divs create staggered / staged division, old setting was divs += t / 0.20; // let the mouse distance control the zoom divs += t / ( ( m.x + 2. ) / iResolution.x ); vec2 div = vec2( divs, divs*iResolution.y/iResolution.x ); vec2 uv = fragCoord.xy / iResolution.xy; // center on screen then pan off: uv -= 0.1 + (iGlobalTime*0.0001); float b = 1.0*divs/iResolution.x; // blur over 2.4 pixels vec2 xy = div*uv; vec2 S; // speed of fundamental vec2 S2; // speed of 1st octave vec2 S3; // speed of 2nd harmonic (perfect fifth?) S.x = (xy.x + xy.y)*(xy.x - xy.y)*0.5; // "velocity potential" S2.x = (xy.x + xy.y)*(xy.x - xy.y)*0.5; // "velocity potential" S3.x = (xy.x + xy.y)*(xy.x - xy.y)*0.5; // "velocity potential" S.y = xy.x*xy.y; // stream function S2.y = xy.x*xy.y; // stream function S3.y = xy.x*xy.y; // stream function // speed of the dots S.x -= iGlobalTime *timespeed; // animate stream S2.x -= iGlobalTime *timespeed + (my * 20. ); // animate stream S3.x -= iGlobalTime *timespeed + (my * 20.); // animate stream // HERE IS THE WAVE HARMONICS // SXY IS FUNDAMENTAL WAVE2 IS 2ND HARMONIC // sxy is *probably* the main wave // wave2 is the 2nd harmonic vec2 sxy = sin(3.14159 * S * 1.0 ); vec2 wave2 = sin(3.14159 * S2 * 2.0 ); // 2.00 is double vec2 wave3 = sin(3.14159 * S3 * 3.0 ); // 3.00 is double // w2 is the 2nd harmonic float a = sxy.x * sxy.y; // combine sine waves using product float w2 = wave2.x * wave2.y; // combine sine waves using product float w3 = wave3.x * wave3.y; // combine sine waves using product // not sure what this does but we will do it to w2, w3 as well a = 0.5*a + 0.5; // remap to [0..1] a = smoothstep( 0.85-b, 0.85+b, a ); // threshold w2 = 0.5*a + 0.5; // remap to [0..1] w2 = smoothstep( 0.85-b, 0.85+b, a ); // threshold w3 = 0.5*a + 0.5; // remap to [0..1] w3 = smoothstep( 0.85-b, 0.85+b, a ); // threshold float c = sqrt( a ); // correct for gamma float w2gamma = sqrt( w2 ); // correct for gamma float w3gamma = sqrt( w3 ); // correct for gamma float red, green, blue; red = sxy.x - sxy.y ; green = wave2.x - wave2.y; blue = wave3.x - wave3.y; float crossover = -1.5; if (red < crossover) { red = red * -1.; } if (green < crossover) { green = green * -1.; } if (blue < crossover) { blue = blue * -1.; } fragColor = vec4( red, green, blue, 1.0); }

# The cosmic consciousness is real…

Posted by tomachi on February 25th, 2017 filed in ScienceComments Off on The cosmic consciousness is real…

### Essentially “the cosmic consciousness” is actually a non-local quantum state of matter!

# China hits 3,000 ppm CO2 on Nullschool Earth Simulator

Posted by tomachi on January 29th, 2017 filed in EnvironmentComments Off on China hits 3,000 ppm CO2 on Nullschool Earth Simulator

This is a screenshot from today on this co-ordinate in Nullschool Earth. COsc means Carbon Dioxide at “surface concentration” and this map also shows SOsc or Silicon Oxide.