[Python] Generate a random matrix in Python which satisfies a condition

I manually define the following 16 matrices in Python :

matrices = {
"Simulation 1": [
[1, 1, 1, 1, 1, 2],
[1, 1, 1, 1, 2, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 2, 3, 2],
[1, 1, 1, 1, 3, 3],
[1, 1, 1, 1, 3, 3]
],

"Simulation 2": [
[1, 1, 2, 2, 2, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 2, 2, 2, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 2, 2, 3],
[1, 1, 1, 3, 3, 3]
],

"Simulation 3": [
[1, 1, 2, 2, 2, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 2, 3, 3],
[1, 1, 2, 2, 3, 3],
[1, 1, 1, 3, 3, 3],
[1, 1, 3, 3, 3, 3]
],

"Simulation 4": [
[1, 1, 1, 1, 2, 2],
[1, 1, 1, 2, 2, 2],
[3, 1, 3, 3, 3, 2],
[3, 3, 3, 3, 3, 2],
[3, 3, 3, 3, 3, 2],
[3, 3, 3, 3, 3, 3]
],

"Simulation 5": [
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 1, 3, 2],
[1, 3, 3, 3, 3, 3],
[3, 3, 3, 3, 3, 3],
[3, 3, 3, 3, 3, 3]
],

"Simulation 6": [
[1, 1, 1, 1, 1, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 1, 2, 2],
[1, 1, 1, 1, 2, 3],
[1, 3, 3, 3, 3, 3],
[1, 3, 3, 3, 3, 3]
],

"Simulation 7": [
[1, 1, 1, 1, 2, 2],
[1, 1, 1, 1, 1, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 3, 2, 2, 3],
[1, 1, 3, 3, 3, 3],
[3, 3, 3, 3, 3, 3]
],

"Simulation 8": [
[1, 1, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 3, 3],
[2, 2, 3, 3, 3, 3],
[2, 2, 2, 3, 3, 3]
],

"Simulation 9": [
[1, 1, 2, 2, 2, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 1, 2, 2],
[1, 1, 1, 1, 3, 2],
[1, 1, 1, 1, 3, 3],
[1, 1, 3, 3, 3, 3]
],

"Simulation 10": [
[1, 1, 1, 2, 2, 2],
[1, 1, 2, 2, 2, 2],
[1, 1, 2, 2, 2, 2],
[1, 1, 2, 2, 2, 3],
[1, 1, 1, 1, 3, 3],
[1, 1, 1, 3, 3, 3]
],

"Simulation 11": [
[1, 1, 1, 2, 2, 2],
[1, 1, 2, 2, 2, 2],
[1, 1, 2, 2, 2, 3],
[1, 1, 1, 2, 3, 3],
[1, 1, 1, 3, 3, 3],
[1, 1, 1, 3, 3, 3]
],

"Simulation 12": [
[1, 1, 1, 1, 2, 2],
[1, 1, 1, 1, 2, 2],
[1, 1, 1, 1, 2, 2],
[3, 1, 1, 3, 3, 3],
[3, 3, 3, 3, 3, 3],
[3, 3, 3, 3, 3, 3]
],

"Simulation 13": [
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 1, 2, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 3, 3, 3],
[1, 3, 3, 3, 3, 3],
[3, 3, 3, 3, 3, 3]
],

"Simulation 14": [
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 1, 1, 2],
[1, 1, 1, 1, 1, 2],
[1, 1, 1, 3, 3, 2],
[1, 3, 3, 3, 3, 3],
[1, 3, 3, 3, 3, 3]
],

"Simulation 15": [
[1, 1, 1, 2, 2, 2],
[1, 2, 2, 2, 2, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 1, 3, 3],
[1, 1, 1, 3, 3, 3],
[1, 1, 1, 3, 3, 3]
],

"Simulation 16": [
[1, 1, 3, 2, 2, 2],
[1, 1, 3, 2, 3, 3],
[1, 1, 3, 3, 3, 3],
[1, 1, 3, 3, 3, 3],
[1, 1, 3, 3, 3, 3],
[1, 1, 3, 3, 3, 3]
]
}


When visualized, these look like this:



Positions in the matrix are understood like this:

positions = [
[1, 2, 3, 4, 5, 6],
[7, 8, 9, 10, 11, 12],
[13, 14, 15, 16, 17, 18],
[19, 20, 21, 22, 23, 24],
[25, 26, 27, 28, 29, 30],
[31, 32, 33, 34, 35, 36]
]


These matrices have the following properties:

• 1 = Red, 2 = Blue, 3 = Green
• Position 1 is always Red, Position 6 is always Blue and Position 36 is always green
• All circles of the same color can reach all other circles of the same color without touching any other color

Here is an example of an invalid matrix (i.e. node 1 (red) can not reach the other red nodes without stepping on blue):



I have the following question: Is there some algorithm which can be used to rapidly generate (random) valid matrices for this problem? Can something like a tree/graph be used which can efficiently generate 100 hundred such solutions?

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