collatz-castle-p5js

Collatz Castle Text Adventure

a text adventure made from the maze that is the Collatz conjecture

It is a work in progress at the moment.

You are randomly placed in somewhere along the tree of the Collatz numbers.

Your first task is to use use 3n + 1 to find your way back to room 1.

This first task can be completed by following a simple rule:

• if your current room is even choose the door that is half that number

• if the current room is odd choose the door that is triple that number plus one

The second task is to pick up an item in room three.

but how do you get from room one to room three?

It is not so easy. The room numbers are not adjacent as on the regular number

line. Rooms 3 and 4 are not next to one another. If you need help use a map.

see a map by Jason Davies

I got the idea from a Douglas Hofstadter lecture where he was counting

Collatz numbers to see how to get from one number to another.

video here

At the moment I have listed the path of rooms to return to room 1, which means you don’t need to do

I need to make a better explanation of the play.

I am using modulo to place objects in the rooms

see it live at:

live here

see the code at:

code here

first made in Python see the code at

the python code

The algorithm for finding neighbors works like this in Python

def collatzNeighbors(num):
    ''' get the collatz neighbors of a number
        return as a immutable tuple'''
    if num%2 ==0:
        # form 3np1 factor
        if (num-1)%3 == 0:       
            #print(num, (num-1)/3, "or", num*2, "or" ,num/2 )
            return ((num-1)/3, num*2, num/2)
        else:
        # not 3np1 factor
            #print(num, "not 3np1", num*2 , "or",num/2)
            return (num*2, num/2)
    else:
        # cant divide by two as its odd so 3np1 and mult by 2
        #print( num, "is odd so 3np1" , num*3+1, "or", num*2)
        return (num*3+1, num*2)
    

an earlier version is on replit where it was created

as this is a retro game I am making a version for the Commodore 64

and as Commodore BASIC does not have a built in mod() function

I am using the

 
 a-int(a/b)*b
 

see this discussion

Here is the neighbors function in Commodore BASIC

 
 5 print"S"
10 print"collatz neighbors"
20 input"your room";a
30 rem check if the room is mod 2
40 if a - int(a/2)*2 = 0 then 100
50 rem not even
55 rem odd rooms only have 2 doors
60 print "room is odd, only 2 doors"
70 print"room 1:", a*3+1
80 print"room 2:", a*2
90 end
100 rem checking if even room -1 mod3
110 if(a -1) - int((a-1)/3)*3 =0 then 20
0
120 rem not 3 n +1 factor only 2 rooms
130 print"room 1", a*2
140 print"room 2", a/2
150 end
200 rem is 3n+1 factor 3 rooms
210 print"room 1:", (a-1)/3
220 print"room 2:", a*2
230 print"room 3:", a/2
250 end


 
 

you can copy and paste into vice c64 I will create another repo with a c64 disk image

• add some more tasks in other rooms
• add a task from room to room
• make a room to room algorithm. A simple path can be current room and other room back to room one and see where they intersect
• improve room description and add more story
• make some random walking Collatz nodes of room and neighbors that stick to one another, for example one node would be [3,10,5,20] and [3,10,6] the 3 and four nodes could be different shapes
• run the rules as a 1 d cellular automata

see the random walking graph

---

need to add some philosophical ideas here