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Draw a list of continuously colored points

I have a list of point and use list_point to draw it. Let’s say

L=[[k,sqrt(k)] for k in range (1000)] list_plot(L)

I'd like to color the points in a continuous way, to remember the order in which they were drawn. Let's say from the black for the first point on the list to the red for the last.

How can I achieve my goal?

Draw a list of continuously colored points

I have a list of point and use list_point to draw it. Let’s say

L=[[k,sqrt(k)] for k in range (1000)]
list_plot(L)

list_plot(L)

I'd like to color the points in a continuous way, to remember the order in which they were drawn. Let's say from the black for the first point on the list to the red for the last.

How can I achieve my goal?