The electric and magnetic fields are vectors, so you can't draw an electromagnetic wave as a simple surface plot or line plot.
Here's my attempt at an incomplete picture of a plane electromagnetic wave that travels parallel to the x-axis. It's a snapshot at one particular point in time. The red arrows indicate the magnitude and direction of
E at various points in the xy-plane. The dashed blue lines indicate where
E is zero.
You have to complete this picture, mentally, as follows:
1.
Every point in the plane, not just the ones shown, has an arrow attached to it, with a magnitude and direction interpolating the pattern that I've sketched.
2. Fill the space above and below the plane of the "paper" with copies of this diagram, stacked one on top of another so that all points in the three-dimensional space have arrows attached to them. The dashed blue lines become planes perpendicular to the x-axis.
3. Make copies of all those diagrams and change the color of the arrows from red to (say) green. Rotate them 90 degrees around the x-axis so the arrows all point towards and away from you, and the y-axis points towards you (that is, it becomes the z-axis), and the x-axis is the same as the other x-axis. This is the magnetic field
B that is associated with this wave. The planes where
E is zero are also the planes where
B is zero.
4. As time passes, the magnitudes and directions of the
E and
B vectors at each point oscillate in such a way that the overall pattern (but
not the arrows themselves!) marches from left to right or from right to left at speed c. At all times, at each point, the red arrow points either up or down, or vanishes momentarily; and the green arrow points either towards or away from you, or vanishes momentarily.
