Misleading plots of elliptic curves

Elliptic curves in cryptography exist as discrete points in finite fields, not continuous curves. While introductory visualizations show dots scattered across a grid, these plots are misleading about density. As field size increases, the actual density of curve points decreases significantly—approximately 1/p for a field of size p. For cryptographic applications using fields of size 2^255 or larger, the probability of random coordinates being on the curve is virtually zero (2^-255).