Current is constant at all points in a parallel circuit

We have to be a little careful working with this question.   Do you mean
that current is "constant" or do you mean it's "the same current" ?

-- If the energy source for the circuit is supplying DC ... like a battery
   or a solar cell ... then the current is 'constant' at every point in the
   circuit.  It's not changing.  It's the same now as it was 10 seconds
   ago.  But it's NOT necessarily the same amount of current everywhere
   in the circuit.

-- If the energy source for the circuit is not supplying DC ... if it's an
   AC generator, or a charged capacitor, or a function generator ...
   then wherever you look in the circuit, the current is constantly
   changing its value at that point.

-- And if there's any place in the circuit where there are components
   connected in parallel, then the current must have different values
   at different points in the circuit. 
   It can't be the same current everywhere. 

You need to be more specific.  i really don't know what a "motion map" is.you can draw a graph of an object's position, distance, displacement, speed,velocity, or acceleration versus time, or you can draw a graph of the object's x-position versus its y-position and not give any information about time at all.if the graph presents position or displacement against time,  then constant velocity is a straight line . . i.e. a line that has  constant slope.if the graph shows speed against time, then constant velocityis a horizontal piece of line.if the graph shows acceleration against time, then constant  velocity is a piece of line that lies on the x-axis . . it's value is zero.