How can I color points in Three JS using OpenGL and Fragment Shaders to depend on the points' distance to the scene origin - three.js

Question

To clarify I am using React, React Three Fiber, Three JS
I have 1000 points mapped into the shape of a disc, and I would like to give them texture via ShaderMaterial. It takes a vertexShader and a fragmentShader. For the color of the points I want them to transition in a gradient from blue to red, the further away points are blue and the closest to origin points are red.
This is the vertexShader:
const vertexShader = `
uniform float uTime;
uniform float uRadius;
varying float vDistance;
void main() {
vec4 mvPosition = modelViewMatrix * vec4(position, 1.0);
vDistance = length(mvPosition.xyz);
gl_Position = projectionMatrix * mvPosition;
gl_PointSize = 5.0;
}
`
export default vertexShader
And here is the fragmentShader:
const fragmentShader = `
uniform float uDistance[1000];
varying float vDistance;
void main() {
// Calculate the distance of the fragment from the center of the point
float d = 1.0 - length(gl_PointCoord - vec2(0.5, 0.5));
// Interpolate the alpha value of the fragment based on its distance from the center of the point
float alpha = smoothstep(0.45, 0.55, d);
// Interpolate the color of the point between red and blue based on the distance of the point from the origin
vec3 color = mix(vec3(1.0, 0.0, 0.0), vec3(0.0, 0.0, 1.0), vDistance);
// Set the output color of the fragment
gl_FragColor = vec4(color, alpha);
}
`
export default fragmentShader
I have tried solving the problem at first by passing an array of normalized distances for every point, but I now realize the points would have no idea how to associate which array index is the distance correlating to itself.
The main thing I am confused about it is how gl_FragColor works. In the example linked the idea is that every point from the vertexShader file will have a vDistance and use that value to assign a unique color to itself in the fragmentShader
So far I have only succeeded in getting all of the points to be the same color, they do not seem to differ based on distance at all