3. Color the points on a plane in the following way:
(1) Choose any positive integer $m$, let $K_{1}, K_{2}, \cdots, K_{m}$ be different circles with non-zero radii, and $K_{i} \subset K_{j}$ or $K_{j} \subset$ $\mathrm{K}_{i}(i \neq j)$;
(2) The color of any point outside a chosen circle is different from the color of any point inside the circle.

Given that there are 2019 points on the plane, and no three points are collinear. Find the maximum number of colors such that the colors of these points satisfy the conditions.
3. According to the problem, the number of colors is no more than 2019.

Below is the proof that 2019 is achievable.
It is easy to prove that circles $K_{1}, K_{2}, \cdots, K_{2019}$ have points of different colors.

Consider all the segments such that all points are endpoints, there are $\frac{2019 \times 2018}{2}$ such segments.

Next, consider the axes of symmetry of these segments, and assume that the selected point is not on any axis of symmetry. Clearly, the distances between this point and all other points are different (the selected point is not on any axis of symmetry), forming a strictly increasing sequence
$0<s_{1}<s_{2}<\cdots<s_{2019}$.
Thus, there exist $r_{i}(i=1,2, \cdots, 2019)$, such that
$s_{1}<r_{1}<s_{2}<r_{2}<\cdots<s_{2019}<r_{2019}$.
Construct 2019 concentric circles with the selected point as the center and $r_{i}(1 \leqslant i \leqslant 2019)$ as the radii.

Obviously, the colors of these circles are determined, and each point has a different color.