Mathematical art.  Standing waves ripple within and without a circle.

Variations are colour, frequencies, amplitudes, and the speed of movement.  One in eight are monochrome.

Ripple / Event Horizon #5


Mathematical animations inspired by cymatics.  

Symmetric waves ripple around a boundary, causing infinitely complex patterns that evolve forever but never repeat.

Variations are the frequencies and amplitudes of waves, the boundary shape, and the velocity of phase shifts.

Some are contained, others escape to infinity.

Ripple / Cymatic #130

Shifting interference patterns resemble something cellular or crystalline at the microscopic level.

Microscopic #11

Spacebar to pause/unpause.

Fractals similar to Julia sets based on iterating the equation:

z(i+1) = a(i) * cos( b(i) *z(i) ) + c(i) *z^(-order) + d(i) 

With z(0) the canvas position, and the parameters a,b,c and d shifting over time and varying with each iteration.

Colour corresponds to the number of iterations before abs(Im(z)) or abs(Re(z)) > 100.

142 possible colour palettes!

Morphology #71

A collaboration between the artist and the collector.

A beautiful fractal that you can explore, recolour and export in high resolution.  

While each edition has a fixed unique shape and default pallete, the collector can pan and zoom into details, select from all the available palettes, and export very high resolution results.

Controls (may only work in 'live' mode):

Mouse drag: Pan
Mouse wheel: Zoom

Double click: Begin slow zoom in / cancel slow zoom
Triple click: Begin slow zoom out

P: Next palette
O: Previous palette

1-6:  Export image as png at (n) times current canvas resolution

Carousel #60

An interactive chaotic attractor based on a circular harmonograph.

This piece rewards patience.  After the initial structure forms, watch the attractor develop as more iterations are added and the details resolve.  The image will continue to refine itself forever; there is no limit on the iteration number.  Pause, unpause, generate and export jpgs at very high resolutons (see controls below).

This is a generalisation of a piece donated to the Edible East science and art trail on our global sustainable food future, and 100% of every sale and secondary royal1ties will be donated to local food banks.

Controls:  

To stop/restart the attractor iterating, press SPACE.
To switch to a high resolution canvas, press 1-9.  The canvas width will become n*1000 by n*1000 (so 2000x2000 if you press '2') and the attractor will restart.
To export the current canvas as a jpeg, press X.
To update the whole image with current data, press U (helpful if using a high resolution).
To invert, press I.

Many worlds #164

Ripple / Event Horizon #25

Ripple / Event Horizon

Ripple / Cymatic #109

Ripple / Cymatic

Microscopic #13

Microscopic

Morphology #31

Morphology

Carousel #8

Carousel

Many worlds #183

Many worlds

Circular harmonographs made from oscillating frequencies and amplitudes.  

A pleasing study in movement.  Perfect loops.  Created using webgl.  Colours, frequencies, numbers of paths and amplitudes vary with each edition, creating a wide variation in moods.

Harmonograph study #4

Harmonograph study #1

Harmonograph study

A study of attractor families transitioning from limit cycles to chaos.  Each image builds its structure then continues to refine itself over time.  Patience can be rewarded.

Variations include the shape of the underlying attractor, the variance within the attractor family and the colours.

High resolution images can be created and exported, the construction can be paused and unpaused, and the image inverted (works best when paused).

Controls:

To stop/restart the attractor iterating, press SPACE.
To switch to a high resolution canvas, press 1-9. The canvas width will become n*1000 by n*1000 (so 2000x2000 if you press '2') and the attractor will restart.
To export the current canvas as a jpeg, press X.
To update the whole image with current data, press U (helpful if using a high resolution).
To invert, press I (pause first).

Bifurcation #4

Bifurcation #1

Bifurcation

Strange attractors throw shapes across the canvas and evolve over time.  Inspired by the 1997 'strange' screensaver from the xscreensavers collection.  

Four different attractor families, three scaling methods (to map the attractor to the finite canvas), seven colour schemes and infinite parameter combinations lead to unique and fascinating shapes and transitions.  The Clifford and de Jong attractors are represented, as well as two attractors of my own.  

The scaling methods are: 'linear' which simply scale the x and y axes by the maximum absolute values, 'arctan' which replaces x and y with atan(x) and atan(y) and 'sin' which replaces x and y with sin(x) and sin(y) to map them both to (-1,1).

Printed on the console you'll see which attractor you have, its equations, the range of values the parameters can take and the scaling method used.  

I hope you are inspired to learn about these systems.

All income from this token will be donated to foodbanks.

Tribute to Strange #75

Tribute to Strange #96

Tribute to Strange

Sinusoidal energy propagates across a frequency spectrum.  A movement study prepared using webgl.

Variations in transmission include frequency, amplitude, hue, saturation and energy.



Transmission #49

Transmission #46

Transmission

A harmonograph study.  Pulsating mathematical art.  Variations include the frequencies and amplitudes, the order of rotational symmetry, and the frequencies of the pulses.

Pulsar #4

Pulsar #1

Pulsar

Confusion matrix

Dive in!

8BIDOU

A chaotic attractor that is more on the 'chaotic' side.  #objkt4objkt day 3.  Artist: instagram.com/generomics @georgemsavva

Star attraction

A generative take on an Easter tradition.  3000x3000 artist: instagram.com/generomics @georgemsavva

Painted egg 3

Hic et Nunc

                                   #rs                                                                                                          
                                 tats                                                                                                          
                              ;librar                                                                                                          
                           y(sp);lib                                                                                                          
                        rary(gglog                                                                                                          
                     o);windows                                                                                                          
                Fonts(Times=w                                                                                                          
          indowsFont("Times                                                                                                          
  New Roman"));poly<-createPolygons("\ua729",font="Times");text<-readChar(sys.frame(1
                   )$ofile,1e5);c                                                                               hars<-unlist(str    
                   split(text,""));                                                                          chars[chars=="        
                   \n"]<-";";char                                                                      s<-chars[chars!           
                   ="\r"];Nx<-10                                                                 0;Ny<-40;d<-ex                
                   pand.grid(x=1                                                             :Nx,y=Ny:1);##                     
                   THE CODE I                                                         S THE ART 3 #                        
                   #;d$inpoly<-a                                                      s.logical(point.i                             
                   n.polygon(d$                                                 x/Nx,(d$y)/Ny,p                                 
                   oly$x,poly$y)                                             );rles<-by(d,-d                                      
                   $y,function(d                                        )rle(d$inpoly)$le                                        
                   ngths);vals<-                                    by(d,-d$y,functi                                             
                   on(d)rle(d$in                                poly)$values);#quine;                                        
                   cumsums<-fu                                             nction(chars)cumsum                             
                   (strwidth(cha                                                              rs,units="inche                     
                   s"));scale=su                                                                      m(d$inpoly)/m                
                   ax(cumsums(                                                                            chars))*1.0             
                   19;#rtistry;sp                                                                               width<-strw          
                   idth(" ", units=                     "inc                                                    hes")*scale*       
                    .9;chars<-c(chars,rep(" ",10                                                       0));getW<-fu     
                     nction(chars,w)which(cu                                                             msums(char     
                           s)>w/scale)[1];fo                                                                   r(r in seq_alo    
                                                                                                                        ng(rles)){;for(i    
                                                                                                                         in seq_along     
                                                                                                                      (rles[[r]])){;if(v     
                                                                                                                   als[[r]][i]==FAL       
                                                                                                                SE) cat(paste0(        
                                                 rep("                                                  ",rles[[r]][i]/spwidt          
                                                    h),collaps                                e=""));if(vals[[r]][i]==T             
                                                         RUE){j=getW(chars,rles[[r]][i]);cat(paste0(ch                 
                                                             ars[1:j],collapse=""));chars<-chars[-(1:j                     
                                                                    )]}};cat("\n")};        


                    ...

                #rstat                                       s;libra                 
         ry(sp);library(gg                      logo);windowsF          
     onts(Times=window               sFont("Times New R     
  oman"));poly<-createPo          lygons("\u2665",font="T   
 imes");text<-readChar(sy      s.frame(1)$ofile,1e5);cha 
rs<-unlist(strsplit(text,""));ch  ars[chars=="\n"]<-";";chars<
-chars[chars!="\r"];Nx<-100;Ny<-31;d<-expand.grid(x=1:
Nx,y=Ny:1);## THE CODE IS THE ART 3 ##;d$inpoly<-a
s.logical(point.in.polygon(d$x/Nx,(d$y)/Ny,poly$x,poly$y
));rles<-by(d,-d$y,function(d)rle(d$inpoly)$lengths);vals 
  <-by(d,-d$y,function(d)rle(d$inpoly)$values);#quine;cu  
   msums<-function(chars)cumsum(strwidth(chars,unit    
     s="inches"));scale=sum(d$inpoly)/max(cumsums(      
        chars))*1.019;#rtistry;spwidth<-strwidth(" ", un        
          its="inches")*scale*.9;chars<-c(chars,rep("#          
            ",100));getW<-function(chars,w)which(cu            
               msums(chars)>w/scale)[1];for(r in seq               
                  _along(rles)){;for(i in seq_along(rle                 
                    s[[r]])){;if(vals[[r]][i]==FALSE) ca                    
                      t(paste0(rep(" ",rles[[r]][i]/sp                      
                         width),collapse=""));if(val                         
                            s[[r]][i]==TRUE){j=get                            
                              W(chars,rles[[r]][i]);                              
                                cat(paste0(char                                
                                  s[1:j],collapse                                  
                                    =""));chars                                     
                                      <-chars[-                                       
                                        (1:j)]}}                                        
                                         ;cat(                                         
                                          "\n"                                           
                                            )}   

george-savva

george-savva

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