Convert to Mind Map Layout

Transform my org chart into a mind map layout where the central idea branches out in all directions.

Framework: [React, Vue, vanilla JS, etc.]
Current code: [paste your existing org chart code or describe it]

Requirements:
1. Central node in the middle of the screen
2. Child nodes branch outward (not just downward like a tree)
3. Automatic layout so nodes don't overlap
4. Curved connecting lines for a natural look
5. Click to expand branches in any direction

Also want:
- Different colors for different branch depths
- Ability to add new nodes by clicking "+" buttons
- Auto-save as users add ideas

This is for a brainstorming app where users build ideas visually.

I'm learning, so explain the difference between tree and radial layouts.