# This example illustrates how to use gnuplot for plotting parametric curves. # We plot the images under the Cayley map z \mapsto (z-i)/(z+i) of lines parallel to # the real and imaginary axis, respectively. # # Author: Konstantin Poelke, 04/2013 # # Switch to parametric mode, then we can plot curves parametrized by t set parametric # Set sample density to smoothen plots set samples 500 # Define some line styles # Line type (lt) is solid line # Line width (lw) should be 3 set style line 1 lt 1 lw 3 linecolor rgb "red" set style line 2 lt 1 lw 3 linecolor rgb "blue" set style line 3 lt 1 lw 3 linecolor rgb "green" # Set scaling of x and y axis of the plot. set xrange[-2:2] set yrange[-2:2] # Real and imaginary part with the x variable being the parameter t # The constant y values are parametrized by some constant c rx(t,c)=(t**2+c**2-1)/(t**2+(c+1)**2) ix(t,c)=-2*t/(t**2+(c+1)**2) # Set first terminal as output set term wxt 0 # Add a title to the plot set title "Lines parallel to the real axis transformed by the Cayley map" # Plot three parametric curves, for different constant values for y=c plot [-50:50] rx(t,1), ix(t,1) ls 1, rx(t,10), ix(t,10) ls 2, rx(t,-2), ix(t,-2) ls 3 # Real and imaginary part, this time with the y variable being the parameter t # The constant x values are parametrized by some constant c ry(c,t)=(c**2+t**2-1)/(c**2+(t+1)**2) iy(c,t)=-2*c/(c**2+(t+1)**2) # Open a second terminal window set term wxt 1 # Add a title to the plot set title "Lines parallel to the imaginary axis transformed by the Cayley map" # Plot three parametric curves, for different constant values for x=c plot [-50:50] ry(1,t), iy(1,t) ls 1, ry(10,t), iy(10,t) ls 2, ry(-2,t), iy(-2,t) ls 3