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 OdeFactory Images and Annotations View/Sys/Gal: EMap "AGF: 1 complex line and a real line, EMap" in "AGFractals."Range: (vMax,vMin) = (6.500,-3.500), (hMin,hMax) = (-4.000,6.500)VFld: AGFThis AGF is generated by the lines:L[1]: (x-1)+(y-1) = 0, m = -1, λ1 = 1I[1]: x+i*y = 0, λ1 = iThe degree of the RHS of the system is: 2.Shift-click on the complex line and on the real line to open slider-based parameter controllers. Vary the 12 control parameters to find interesting EMap variations.In general a 2D polynomial system has 2*(3+2+1) = 12 control parameters. The 2D Mandelbot system, z <- z^2+c, has only 2 control parameters.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 1 complex line and a real line, ver 2, EMap" in "AGFractals."Range: (vMax,vMin) = (3.919,-3.826), (hMin,hMax) = (-2.484,4.823)VFld: AGFThis AGF is generated by the lines:L[1]: (x-1.2)+0.10753*(y-1) = 0, m = -9.3, λ1 = 0.9I[1]: x+i*y = 0, λ1 = (0.14+i)The degree of the RHS of the system is: 2.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 2 complex lines, EMap" in "AGFractals."Range: (vMax,vMin) = (1.455,-3.545), (hMin,hMax) = (-2.094,2.906)VFld: AGFThis AGF is generated by the lines:I[1]: (x-1)+i*y = 0, λ1 = iI[2]: (x+1)+i*y = 0, λ2 = (1-i)The degree of the RHS of the system is: 3.Image 1: Ode R2+ view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 2 complex lines, in dx/dt, dy/dt form, EMap" in "AGFractals."Range: (vMax,vMin) = (1.450,-3.550), (hMin,hMax) = (-2.090,2.910)VFld: ((1-x^2+x^3+y^2+x*(-1+4 *y+y^2))/4,(x^2*(-2+y)-2*x*y+(2+y) *(1+y^2))/4)This system of odes is defined by:dx/dt = (1-x^2+x^3+y^2+x*(-1+4*y+y^2))/4,dy/dt = (x^2*(-2+y)-2*x*y+(2+y)*(1+y^2))/4.It is the same as the previous AGF but it is has been rewritten in the traditional dx/dt, dy/dt form.Image 1: EMap view. View/Sys/Gal: EMap "AGF: 2 complex lines, ver 2, EMap" in "AGFractals."Range: (vMax,vMin) = (1.443,-4.145), (hMin,hMax) = (-2.845,2.428)VFld: AGFThis system is the result of adjusting the 8 parameters for I[1] in system:        AGF: 2 complex lines, EMapThe AGF is generated by the lines:I[1]: (1.1+0.01*i)*(x-0.9)+(0.12+0.8*i)*(y-0.01) = 0, λ1 = (0.03+1.2*i)I[2]: (x+1)+i*y = 0, λ2 = (1-i)The degree of the RHS of the system is: 3.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 2 complex lines, ver 3, EMap" in "AGFractals."Range: (vMax,vMin) = (2.440,-1.800), (hMin,hMax) = (-1.950,2.410)VFld: AGFThis AGF is generated by the lines:I[1]: 1.43*(x-1)+1.2*i*y = 0, λ1 = (1.3-0.4*i)I[2]: 1.1*(x+1)+i*y = 0, λ2 = (-1.56+0.99*i)The degree of the RHS of the system is: 3.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 2 complex lines, ver 4, EMap" in "AGFractals."Range: (vMax,vMin) = (0.532,-0.872), (hMin,hMax) = (-1.205,0.013)VFld: AGFThis AGF is generated by the lines:I[1]: 1.43*(x-1)+1.2*i*y = 0, λ1 = (1.3-0.4*i)I[2]: 1.1*(x+1)+i*y = 0, λ2 = (-1.56+0.99*i)The degree of the RHS of the system is: 3.Image 1: Ode R2+ view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 2 complex lines, ver 5, EMap" in "AGFractals."Range: (vMax,vMin) = (1.760,-1.206), (hMin,hMax) = (-0.193,1.682)VFld: AGFThis AGF is generated by the lines:I[1]: (1.1+0.01*i)*(x-1)+(0.01+0.8*i)*y = 0,         λ1 = (0.01+1.1*i)I[2]: (x+1.4)+(-0.01+0.7*i)*y = 0,          λ2 = (1-1.1*i)The degree of the RHS of the system is: 3.Image 1: Ode R2+ view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 2 complex lines, ver 6, EMap" in "AGFractals."Range: (vMax,vMin) = (0.641,-0.641), (hMin,hMax) = (0.407,1.600)VFld: AGFThis AGF is generated by the lines:I[1]: (x-1)+i*y = 0, λ1 = (0.005+i)I[2]: (x+1)+i*y = 0, λ2 = (1-i)The degree of the RHS of the system is: 3.Image 1: Ode R2+ view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 2 complex lines, ver 7, EMap" in "AGFractals."Range: (vMax,vMin) = (2.705,-2.295), (hMin,hMax) = (-2.557,2.443)VFld: AGFThis AGF is generated by the lines:        I[1]: 1.4*(x-1)+1.2*i*y = 0,          λ1 = (1.9-0.07*i)        I[2]: 1.1*(x+1)+i*y = 0,          λ2 = (-1.56+0.99*i)The degree of the RHS of the system is: 3.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 3 complex lines" in "AGFractals."Range: (vMax,vMin) = (3.000,-2.000), (hMin,hMax) = (-2.500,2.500)VFld: AGFThis AGF is generated by the lines:        I[1]: x+i*(y-1) = 0, λ1 = i        I[2]: (x-1)+i*y = 0, λ2 = i        I[3]: (x+1)+i*y = 0, λ3 = iThe degree of the RHS of the system is: 5.This is an interesting Ode but it is not so interesting in the IMap or EMap views.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 3 complex lines, 1 real line" in "AGFractals."Range: (vMax,vMin) = (2.500,-2.500), (hMin,hMax) = (-2.500,2.500)VFld: AGFThis AGF is generated by the lines:        L[1]: x-y = 0, m = 1, λ1 = 0.01        I[1]: x+i*(y-1) = 0, λ1 = (-0.1+i)        I[2]: (x-1)+i*y = 0, λ2 = (-0.1+i)        I[3]: (x+1)+i*y = 0, λ3 = (0.1+i)The degree of the RHS of the system is: 6.Another interesting Ode.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 3 complex lines, 1 real line, ver 2" in "AGFractals."Range: (vMax,vMin) = (1.801,-0.699), (hMin,hMax) = (-1.337,1.163)VFld: AGFThis AGF is generated by the lines:        L[1]: x-y = 0, m = 1, λ1 = -0.01        I[1]: x+i*(y-1) = 0, λ1 = (-0.1+i)I[2]: (1-0.3*i)*(x+0.3)+i*(y-0.82) = 0,          λ2 = (-0.1-1.1*i)        I[3]: (x+1)+i*y = 0, λ3 = (0.1+i)The degree of the RHS of the system is: 6.An interesting Ode and EMap.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 3 complex lines, ver 2, EMap" in "AGFractals."Range: (vMax,vMin) = (2.200,-1.800), (hMin,hMax) = (-1.800,2.200)VFld: AGFThis AGF is generated by the lines:        I[1]: x+i*(y-1) = 0, λ1 = iI[2]: (-2+0.5*i)*(x-1)+(0.3+2.01*i)*y = 0,          λ2 = (-0.15+1.4*i)        I[3]: (x+1)+i*y = 0, λ3 = iThe degree of the RHS of the system is: 5.Sort of an interesting Ode but a more interesting EMap.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 3 complex lines, ver 3, EMap" in "AGFractals."Range: (vMax,vMin) = (2.469,-1.531), (hMin,hMax) = (-1.652,2.073)VFld: AGFThis AGF is generated by the lines:I[1]: (1.0001+1.2*i)*(x-0.001)+(0.5001+2*i)*(y-1.0001) = 0, λ1 = (-2.06-0.45*i)        I[2]: (x-1)+i*y = 0, λ2 = i        I[3]: (x+1)+i*y = 0, λ3 = iThe degree of the RHS of the system is: 5.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 3 complex lines, ver 4, EMap" in "AGFractals."Range: (vMax,vMin) = (1.800,-1.800), (hMin,hMax) = (-1.700,2.000)VFld: AGFThis AGF is generated by the lines:        I[1]: x+i*(y-1) = 0, λ1 = iI[2]: (1-0.01*i)*(x-1)+(-0.04+i)*(y-0.03) = 0,          λ2 = (-0.51-1.4*i)        I[3]: (x+1)+i*y = 0, λ3 = iThe degree of the RHS of the system is: 5.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 3 real lines" in "AGFractals."Range: (vMax,vMin) = (10.000,-10.000), (hMin,hMax) = (-10.000,10.000)VFld: AGFThis AGF is generated by the lines:L[1]: x-(y+1) = 0, m = 1, λ1 = 1L[2]: x+(y+1) = 0, m = -1, λ2 = 1L[3]: (y-1) = 0, m = 0, λ3 = 1The degree of the RHS of the system is: 2.Image 1: Ode view.Image 2: EMap view. View/Sys/Gal: EMap "AGF: 3 real lines, ver 2, EMap" in "AGFractals."Range: (vMax,vMin) = (1.355,-0.542), (hMin,hMax) = (-0.432,1.107)VFld: AGFThis AGF is generated by the lines:L[1]: x-0.2381*(y+1) = 0, m = 4.2, λ1 = 1.2L[2]: x+(y+1) = 0, m = -1, λ2 = -5L[3]: (y-1) = 0, m = 0, λ3 = -1The degree of the RHS of the system is: 2.Image 1: Ode R2+ view.Image 2: EMap view. View/Sys/Gal: EMap "AGFv: variation 1 of star-in & star-out, EMap" in "AGFractals."Range: (vMax,vMin) = (5.400,-5.700), (hMin,hMax) = (-10.000,10.000)VFld: (b*x^2-y^2+p,a*x*y%c+q), p = -.70; q = 1.00; a = 1.00; b = .30; c = 6.70; This system of odes is defined by the equations:        dx/dt = b*x^2-y^2+p,        dy/dt = a*x*y%c+qParameters are:         p = -.70; q = 1.00; a = 1.00;         b = .30; c = 6.70;Image 1: Ode view with colored V fld on.Image 2: EMap view. View/Sys/Gal: EMap "AGFv: variation 2 of star-in & star-out, EMap" in "AGFractals."Range: (vMax,vMin) = (1.250,-1.250), (hMin,hMax) = (-1.250,1.250)VFld: (x^2-y^2+p,2*x%y+q), p = -.65; q = 1.00; This system of odes is defined by the equations:        dx/dt = x^2-y^2+p,        dy/dt = 2*x%y+qParameters are:         p = -.65; q = 1.00;Image 1: Ode view with colored V fld on.Image 2: EMap view.