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OdeFactory Images and Annotations  
View/Sys/Gal: EMap "AGF: 1 complex line and a real line, EMap" in "AGFractals." This AGF is generated by the lines: L[1]: (x1)+(y1) = 0, m = 1, λ_{1} = 1 I[1]: x+i*y = 0, λ_{1} = i The degree of the RHS of the system is: 2. Shiftclick on the complex line and on the real line to open sliderbased 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." This AGF is generated by the lines: L[1]: (x1.2)+0.10753*(y1) = 0, m = 9.3, λ_{1} = 0.9 I[1]: x+i*y = 0, λ_{1} = (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." This AGF is generated by the lines: I[1]: (x1)+i*y = 0, λ_{1} = i I[2]: (x+1)+i*y = 0, λ_{2} = (1i) 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." This system of odes is defined by: dx/dt = (1x^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." This system is the result of adjusting the 8 parameters for I[1] in system: AGF: 2 complex lines, EMap The AGF is generated by the lines: I[1]: (1.1+0.01*i)*(x0.9)+(0.12+0.8*i)*(y0.01) = 0, λ_{1} = (0.03+1.2*i) I[2]: (x+1)+i*y = 0, λ_{2} = (1i) 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." This AGF is generated by the lines: I[1]: 1.43*(x1)+1.2*i*y = 0, λ_{1} = (1.30.4*i) I[2]: 1.1*(x+1)+i*y = 0, λ_{2} = (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." This AGF is generated by the lines: I[1]: 1.43*(x1)+1.2*i*y = 0, λ_{1} = (1.30.4*i) I[2]: 1.1*(x+1)+i*y = 0, λ_{2} = (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." This AGF is generated by the lines: I[1]: (1.1+0.01*i)*(x1)+(0.01+0.8*i)*y = 0, λ_{1} = (0.01+1.1*i) I[2]: (x+1.4)+(0.01+0.7*i)*y = 0, λ_{2} = (11.1*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." This AGF is generated by the lines: I[1]: (x1)+i*y = 0, λ_{1} = (0.005+i) I[2]: (x+1)+i*y = 0, λ_{2} = (1i) 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." This AGF is generated by the lines: I[1]: 1.4*(x1)+1.2*i*y = 0, λ_{1} = (1.90.07*i) I[2]: 1.1*(x+1)+i*y = 0, λ_{2} = (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." This AGF is generated by the lines: I[1]: x+i*(y1) = 0, λ_{1} = i I[2]: (x1)+i*y = 0, λ_{2} = i I[3]: (x+1)+i*y = 0, λ_{3} = i The 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." This AGF is generated by the lines: L[1]: xy = 0, m = 1, λ_{1} = 0.01 I[1]: x+i*(y1) = 0, λ_{1} = (0.1+i) I[2]: (x1)+i*y = 0, λ_{2} = (0.1+i) I[3]: (x+1)+i*y = 0, λ_{3} = (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." This AGF is generated by the lines: L[1]: xy = 0, m = 1, λ_{1} = 0.01 I[1]: x+i*(y1) = 0, λ_{1} = (0.1+i) I[2]: (10.3*i)*(x+0.3)+i*(y0.82) = 0, λ_{2} = (0.11.1*i) I[3]: (x+1)+i*y = 0, λ_{3} = (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." This AGF is generated by the lines: I[1]: x+i*(y1) = 0, λ_{1} = i I[2]: (2+0.5*i)*(x1)+(0.3+2.01*i)*y = 0, λ_{2} = (0.15+1.4*i) I[3]: (x+1)+i*y = 0, λ_{3} = i The 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." This AGF is generated by the lines: I[1]: (1.0001+1.2*i)*(x0.001)+(0.5001+2*i)*(y1.0001) = 0, λ_{1} = (2.060.45*i) I[2]: (x1)+i*y = 0, λ_{2} = i I[3]: (x+1)+i*y = 0, λ_{3} = i The 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." This AGF is generated by the lines: I[1]: x+i*(y1) = 0, λ_{1} = i I[2]: (10.01*i)*(x1)+(0.04+i)*(y0.03) = 0, λ_{2} = (0.511.4*i) I[3]: (x+1)+i*y = 0, λ_{3} = i The 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." This AGF is generated by the lines: L[1]: x(y+1) = 0, m = 1, λ_{1} = 1 L[2]: x+(y+1) = 0, m = 1, λ_{2} = 1 L[3]: (y1) = 0, m = 0, λ_{3} = 1 The 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." This AGF is generated by the lines: L[1]: x0.2381*(y+1) = 0, m = 4.2, λ_{1} = 1.2 L[2]: x+(y+1) = 0, m = 1, λ_{2} = 5 L[3]: (y1) = 0, m = 0, λ_{3} = 1 The 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 starin & starout, EMap" in "AGFractals." This system of odes is defined by the equations: dx/dt = b*x^2y^2+p, dy/dt = a*x*y%c+q Parameters 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 starin & starout, EMap" in "AGFractals." This system of odes is defined by the equations: dx/dt = x^2y^2+p, dy/dt = 2*x%y+q Parameters are: p = .65; q = 1.00; Image 1: Ode view with colored V fld on. Image 2: EMap view.
