Rule 30 is a one-dimensional binary cellular automaton. You can have some information here:
You have to write a function that takes as input an array of 0 and 1 and a positive integer that represents the number of iterations. This function has to performe the nth iteration of the Rule 30 with the given input.
The rule to derive a cell from itself and its neigbour is:
| Current cell | 000 | 001 | 010 | 011 | 100 | 101 | 110 | 111 |
|---|---|---|---|---|---|---|---|---|
| New cell | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
As you can see the new state of a certain cell depends on his neighborhood. In Current cells you have the nth cell with his left and right neighbor, for example the first configuration is 000:
- left neighbor = 0
- current cell = 0
- right neighbor = 0
The result for the current cell is 0, as reported in New cell row.
You also have to pay attention to the following things:
- the borders of the list are always 0
- values different from 0 and 1 must be considered as 0
- a negative number of iteration never changes the initial sequence
- you have to return an array of 0 and 1
Here a small example step by step, starting from the list [1] and iterating for 5 times:
- We have only one element so first of all we have to follow the rules adding the border, so the result will be [0, 1, 0]
- Now we can apply the rule 30 to all the elements and the result will be [1, 1, 1] (first iteration)
- Then, after continuing this way for 4 times, the result will be [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]
In Python, you can also use a support function to print the sequence named printRule30. This function takes as parameters the current list of 0 and 1 to print, the max level that you can reach (number of iterations) and the length of initial array.
def printRule30(list_, maxLvl, startLen):
...The last two parameters are optional and are useful if you are printing each line of the iteration to center the result like this:
░░▓░░ -> step 1
░▓▓▓░ -> step 2
▓▓░░▓ -> step 3
If you pass only the array of 0 and 1 the previous result for each line will be like this:
▓ -> step 1
▓▓▓ -> step 2
▓▓░░▓ -> step 3
Note: the function can print only the current list that you pass to it, so you have to use it in the proper way during the interactions of the rule 30.