A quick script to plot the density of points when placing points in [-1, 1] greedily to maximize distance from previous points.

points.py

import numpy as np
from scipy import optimize
from tqdm import tqdm
from matplotlib import pyplot as plt

NUM_POINTS = 1000
STEP = 0.001
BIN_SIZE = 0.05

grid = np.reshape(np.arange(-1, 1 + STEP, STEP), (-1, 1))
points = [-1]
for _ in tqdm(range(NUM_POINTS)):
    ps = np.reshape(points, (1, -1))
    dists = np.abs(ps - grid)
    prods = np.prod(dists, axis=1)
    max_ind = np.argmax(prods)
    points.append(grid[max_ind, 0])

bins = np.arange(-1, 1+BIN_SIZE, BIN_SIZE)
plt.hist(points, bins=bins)
plt.show()