Write a formular on aprogram to generate the following patterns

To generate various patterns, you can use loops and conditional statements in a programming language. Here's an example of generating a few common patterns using Python:

Pattern 1: Square Pattern

```python
# Taking input for the number of rows and columns
rows = int(input("Enter the number of rows: "))
columns = int(input("Enter the number of columns: "))

# Generating the square pattern
for i in range(rows):
for j in range(columns):
print('*', end='')
print()
```

Pattern 2: Right Triangle Pattern

```python
# Taking input for the number of rows
rows = int(input("Enter the number of rows: "))

# Generating the right triangle pattern
for i in range(rows):
for j in range(i+1):
print('*', end='')
print()
```

Pattern 3: Hollow Square Pattern

```python
# Taking input for the number of rows and columns
rows = int(input("Enter the number of rows: "))
columns = int(input("Enter the number of columns: "))

# Generating the hollow square pattern
for i in range(rows):
for j in range(columns):
if i == 0 or i == rows-1 or j == 0 or j == columns-1:
print('*', end='')
else:
print(' ', end='')
print()
```

These are just a few examples of patterns, and you can customize them by changing the program logic or adding conditions based on your desired pattern.