# WCCChallenge_SwissDesign # Lines+Colors For this week's Creative Code Challenge by **@sableraph: "Swiss Design”, Lines+Colors** is coded in ***Hydra & SonicPi.*** It uses linear algebra concepts in both the visuals and audio to make the piece. This is inspired and uses Cramer rule as a focal point. ## Colors as Building Blocks Gabriel Cramer is a swiss mathematician which the rule is named after as it is used in solving systems of linear equations: [https://en.wikipedia.org/wiki/Cramer%27s\_rule](https://en.wikipedia.org/wiki/Cramer%27s_rule) . In addition to this rule, the audiovisual components are controlled b[y](https://en.wikipedia.org/wiki/Cramer%27s_rule) various properties and aspects of matrices [(](https://en.wikipedia.org/wiki/Cramer%27s_rule)inverse, normal, linear transformations,etc) This can be seen as the visuals are intersecting color lines and in the audio, colors are grouped into sets to make new colors and connections. Which is then carried on in [](https://en.wikipedia.org/wiki/Cramer%27s_rule)the composition. ## Poem ```ocaml Colours reflecting Colours intersecting Rebuilding with the excerpts That have joined the intersects What combinations can be heard? What information can be unearthed? What new patterns can be birthed? Some pleasant and others absurd? ``` ## Video ## Code ### Hydra ```javascript var y = prompt("choose between number 0 - 39") //3 x 3 matrix based on the y prompt pos = [y*2,y-21,y,y+3,Math.abs(y-7),y+5,y/4, y/5+2, y-14] a = pos[0] b = pos[1] c = pos[2] d = pos[3] e = pos[4] f = pos[5] g = pos[6] h = pos[7] i = pos[8] //recoding into Matrix Coordinates A11 = a A12 = b A13 = c A21 = d A22 = e A23 = f A31 = g A32 = h A33 = i //determinant formula det_a = a*(e*i - f*h) - b*(d*i - f*g) + c*(d*h - e*g) trace = a + e + i normal = Math.sqrt(a*a + b*b + c*c + d*d + e*e + f*f + g*g + h*h + i*i) //Adjoint Formula Adj_a = (A22*A33 - A23*A32) Adj_b = -1 * (A12*A33 - A13 * A32) Adj_c = A12 *A23 - A13*A22 Adj_d = -1 * (A21 * A33 - A23 *A31) Adj_e = (A11 *A33 - A13 * A31) Adj_f = -1 * (A11 * A23 - A13 *A21) Adj_g = (A21 * A32 - A22 *A31) Adj_h = -1 *(A11 * A32 - A12 *A31) Adj_i = (A11 *A22 - A12 *A21) //inverse formula /*A-1 = (adj A)/(det A)*/ inv_a = Adj_a/det_a inv_b = Adj_b/det_a inv_c = Adj_c/det_a inv_d = Adj_d/det_a inv_e = Adj_e/det_a inv_f = Adj_f/det_a inv_g = Adj_g/det_a inv_h = Adj_h/det_a inv_i = Adj_i/det_a shape(()=> normal/trace,trace/det_a,1) .scale(0.5,1).colorama() .color([0.5,2].smooth(1),[0.15,0.35,0.14,1,1.25].smooth(),[0.25,0.5,0.12,0.05,2,4]) .repeat(()=> det_a,trace) .modulateScale(osc(3,0.5),-0.6) .add(o0,0.5) .scale([inv_a/inv_b,inv_c/inv_d].smooth()) .out() speed = inv_d ``` ### SonicPi ```ruby #Colors pair 1 Aqua = [0,255,255] Coral = [255,127,80] #Colors Pair 2 Lavender = [230, 230, 250] Gold = [255,215,0] #Colors Pair 3 MidnightBlue = [25,25,112] DarkOrange = [255,140,0] #Colors Pair 4 SlateGray = [112, 128, 144] Crimson = [220,20,60] def linear_transform(matrixA,vectorA) #this is the first row of the matrix row1 = matrixA[0] #this is the second row of the matrix row2 = matrixA[1] #this is the third row of the matrix row3 = matrixA[2] #this is the first val of the vector vec_x = vectorA[0] #this is the second val of the vector vec_y = vectorA[1] #this is the third val of the vector vec_z = vectorA[2] #this is the first value of the new vector vec_x_formed = [row1[0]*vec_x + row1[1]*vec_y + row1[2]*vec_z] #this is the second value of the new vector vec_y_formed= [row2[0]*vec_x + row2[1]*vec_y + row2[2]*vec_z] #this is the third value of the new vector vec_z_formed = [row3[0]*vec_x + row3[1]*vec_y + row3[2]*vec_z] #new vector vec_change = [vec_x_formed[0],vec_y_formed[0],vec_z_formed[0]] end def color_det2(loop,row1,row2,spread1,spread2) #Cramers Rule with Colors x1a = row1[0] x2a = row1[1] b_a = row1[2] x1b = row2[0] x2b = row2[1] b_b = row2[2] #determinant of main matrix [x1a,x2a,x1b,x2b] det_a = ((x1a * x2b) - (x2a * x1b)).to_f #determinant of main matrix but first column replace by b_a & b_B det_b = (b_a * x2b) - (x2a * b_b) #determinant of main matrix but second column replace by b_a & b_B det_c = (x1a * b_b) - (b_a * x1b) #the solving of the above equations det_1 = det_b/det_a det_2 = det_c/det_a puts det_1 puts det_2 live_loop loop do use_random_seed Time.now.to_i with_fx :ping_pong, mix: rrand(0.4,0.65) do sample :ambi_choir, rate: det_1,beat_stretch: (det_2).abs, pitch: det_1/det_2 if spread(spread1,spread2).tick sleep [(det_1+det_2).abs, (spread1/spread2) + 0.5].choose end with_fx :echo do use_synth :piano play det_2/det_1 end end end def color_det(loop,row1,row2) #Cramers Rule with Colors x1a = row1[0] x2a = row1[1] b_a = row1[2] x1b = row2[0] x2b = row2[1] b_b = row2[2] #determinant of main matrix [x1a,x2a,x1b,x2b] det_a = ((x1a * x2b) - (x2a * x1b)).to_f #determinant of main matrix but first column replace by b_a & b_B det_b = (b_a * x2b) - (x2a * b_b) #determinant of main matrix but second column replace by b_a & b_B det_c = (x1a * b_b) - (b_a * x1b) #the solving of the above equations det_1 = det_b/det_a det_2 = det_c/det_a puts det_1 puts det_2 sample live_loop loop do use_random_seed Time.now.to_i with_fx :ping_pong, mix: rrand(0.4,0.65) do sample [:ambi_choir,:glitch_perc3,:bass_woodsy_c].choose, rate: [det_1,det_2].choose,beat_stretch: [(det_2).abs,(det_1).abs].tick, pitch: [det_1/det_2,det_2/det_1].choose sleep (det_1+det_2).abs use_synth :piano play (det_1/det_2).abs with_fx :krush do use_synth :prophet play (det_2/det_1).abs end end end end #this mathematical sections turns the combo of Aqua, Lavender, Gold into Cyber Neon Green #R,G,B(0,250,40) color_matrix1 = [Aqua, Lavender, Gold] first_vector = [1,-1,1] CyberNeonGreen = linear_transform(color_matrix1,first_vector) #0,250, 40 #this mathematical sections turns the combo of SlateGray, DarkOrange, MidnightBLue into SoftPink color_matrix2 = [SlateGray, DarkOrange, MidnightBlue] second_vector = [1,-1,1.75] SoftPink = linear_transform(color_matrix2,second_vector) #236,115,196 color_matrix3 = [Crimson, SlateGray, Coral] third_vector = [0.5,1,2] CucumberIce = linear_transform(color_matrix3,third_vector) #210,216,160.5 https://icolorpalette.com/color/d2d8a1 #getting the traces color_mx1_trace = color_matrix1[0][0] + color_matrix1[1][1] + color_matrix2[2][2] color_mx2_trace = color_matrix2[0][0] + color_matrix2[1][1] + color_matrix2[2][2] color_mx3_trace = color_matrix3[0][0] + color_matrix3[1][1] + color_matrix3[2][2] live_loop :ColorBending do use_random_seed Time.now.to_i / 2 with_fx :whammy, mix: 0.25 do color_det(:aquaVcoral,Aqua,Coral) sleep [0.5,1,4].choose color_det(:LavenderVgold, Lavender, Gold) sleep [0.5,1,2].choose color_det(:MidnightvsOrange,MidnightBlue, DarkOrange) sleep 2 color_det(:GrayvCrimson,SlateGray, Crimson) sleep [1,2].choose end with_fx :hpf do with_fx [:wobble,:ping_pong].choose, mix: rrand(0.2,0.6) do with_fx [:ping_pong,:vowel].choose, mix: rrand(0.25,0.75) do color_det(:aquaVGold,Aqua,Gold) sleep [2,4,8].choose color_det(:CrimsonVcoral,Crimson,Coral) sleep [2,4,8].choose color_det(:LavenderVOrange,DarkOrange, Lavender) color_det(:GrayvBlue,SlateGray, MidnightBlue) end end end sleep [0.5,1,2,4].choose end live_loop :colortwisting do with_fx :echo, mix: 0.65 do with_fx :ping_pong do color_det2(:CybervsSoft,CyberNeonGreen,SoftPink,color_mx1_trace,color_mx2_trace) sleep [2,4,8].choose color_det2(:IcevsWarmth,SoftPink,CucumberIce,color_mx2_trace,color_mx3_trace) sleep [2,4,8].choose color_det2(:IcevsCyber,CucumberIce,CyberNeonGreen,color_mx3_trace,color_mx1_trace) sleep [3,6,9].choose end end sleep [0.5,1,2].choose end #//3 x 3 matrix sound by random numbers between 0 & 30 live_loop :choirflow do use_random_seed Time.now.to_i y = rrand(0,30) puts y pos = [y*2,y-21,y,y+3,(y-7).abs,y+5,y/4, y/5+2, y-14] a = pos[0] b = pos[1] c = pos[2] d = pos[3] e = pos[4] f = pos[5] g = pos[6] h = pos[7] i = pos[8] #//recoding into Matrix Coordinates A11 = a A12 = b A13 = c A21 = d A22 = e A23 = f A31 = g A32 = h A33 = i #//determinant formula det_a = a*(e*i - f*h) - b*(d*i - f*g) + c*(d*h - e*g) trace = a + e + i normal = Math.sqrt(a*a + b*b + c*c + d*d + e*e + f*f + g*g + h*h + i*i) #//Adjoint Formula Adj_a = (A22*A33 - A23*A32) Adj_b = -1 * (A12 * A33 - A13 * A32) Adj_c = A12 * A23 - A13 * A22 Adj_d = -1 * (A21 * A33 - A23 * A31) Adj_e = (A11 * A33 - A13 * A31) Adj_f = -1 * (A11 * A23 - A13 * A21) Adj_g = (A21 * A32 - A22 * A31) Adj_h = -1 *(A11 * A32 - A12 * A31) Adj_i = (A11 * A22 - A12 * A21) #inverse formula #*A-1 = (adj A)/(det A)*/ inv_a = Adj_a/det_a inv_b = Adj_b/det_a inv_c = Adj_c/det_a inv_d = Adj_d/det_a inv_e = Adj_e/det_a inv_f = Adj_f/det_a inv_g = Adj_g/det_a inv_h = Adj_h/det_a inv_i = Adj_i/det_a sample :ambi_choir, decay: Adj_a.abs, rate: inv_a sample [:ambi_choir,:loop_breakbeat].choose , decay: Adj_b.abs, rate: inv_b sample :ambi_choir , decay: Adj_c.abs, rate: inv_c sleep [1,2,4,8].choose sample [:ambi_choir,:tabla_ghe3].tick , decay: Adj_d.abs, rate: inv_d sample :ambi_choir , decay: Adj_e.abs, rate: inv_e sample [:ambi_choir,:loop_weirdo].choose , decay: Adj_f.abs, rate: inv_f sleep [4,8,16].choose puts inv_i sleep [0.5,1,2,4].choose end ``` ```ruby live_loop :remix do use_random_seed Time.now.to_i/3 #making true random as it goes with the actual time puts Time.now.to_i with_fx :echo, mix: rrand(0.4,0.8) do sample "Line+Color.wav", sustain: dice(10) end sleep [0.25,0.5,1,2,4].choose end live_loop :remix2 do use_random_seed Time.now.to_i/3 #making true random as it goes with the actual time puts Time.now.to_i with_fx [:ping_pong,:whammy,:pitch].choose, mix: rrand(0.1,0.5) do sample "Line+Color.wav", rate: rrand(-2,2.4) - 0.1 end sleep [8,16,24].choose end ```