Certainly! Here's a test case generator for the given problem statement "Avant-garde Art":

```python
import random

def tcgen():
    n = random.choice([i for i in range(2, 8001, 2)])  # Even number between 2 and 8000
    
    k = random.randint(0, min(n // 2, 20))
    
    # Generate an array a such that a[a[i]] = i and a[i] != i
    available = list(range(1, n + 1))
    
    a = [0] * n
    
    def pair_and_assign():
        if len(available) < 2:
            return
        
        i = available.pop(random.randint(0, len(available) - 1))
        j = available.pop(random.randint(0, len(available) - 1))
        
        a[i - 1] = j
        a[j - 1] = i

    while available:
        pair_and_assign()
    
    return n, k, a

# Example usage:
n, k, a = tcgen()
print(n, k)
print(" ".join(map(str, a)))
```

This script will generate test cases for the "Avant-garde Art" problem. Here’s a breakdown of what it does:

1. **Select `n`**: Randomly choose an even number `n` between 2 and 8000.
2. **Select `k`**: Randomly choose `k` within the range from 0 to the minimum of `n/2` and 20.
3. **Generate `a`**: Create the list `a` such that each `a[i]` is connected to a different coordinate, ensuring `a[a[i]] = i` and `a[i] != i`. This list is generated by randomly pairing available coordinates until all are paired.
   
The last part of the script outputs a generated test case. You can call `tcgen()` multiple times to generate multiple test cases.