1. Induced charge distribution of metallic sphere
Feng lei

3. What is a chromatic image supposed to be ?
M ×N
A colorized image is a matrix which has a dimension of 3 ×M ×N , and the index of which represents corresponding pixel.
Each M ×N matrix is supposed to be a color element matrix of the image in RGB color space.

4. RGB color space A specified color has three elements: ZR (0,1)
ZG (0,1)
ZB (0,1)
To illustrate the density of charge by color, we have to define a spectrum of these colors first.

5. There are many ways to make a color band
There are many ways to make a color band. I only choose one plane (ZR-ZB) of RGB color space to define my spectrum.

6. How to convert induced charge density to color distribution ?
The simplest way is to find a linear relation between them.
Then I get that k must be the maximum of σ.

7. How will R/d change the relative density ?
R/d varying in the scope of (0.1,0.9) and θ∈(-Pi , Pi).

8. What dose it look like in the mapping plane?
x-y
y-z
R/d=0.1
R/d=0.3
R/d=0.7

9. What about the condition near the limit point ?
R/d=0.9
R/d=0.99
Those induced charges just appears locating on one point.

10. Let’s do something more interesting!
How about adding another two point charges outside the metallic sphere?
R/d=0.4

11. How about adding two negative point charges outside the metallic sphere?
R/d=0.4

12. How about just changing the distance of the point charge outside the metallic sphere?
R/d=0.3
R/d=0.7

13. Y-Z
Finally, here are two interesting graphs mapped in y-z plane. Can you guess how the point charges locate?

14. Actually , it’s the situation below:

15. Thanks for your attention!
It is wrong but gorgeous anyway.