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Some FRACTRAN programs in case we ever have a category for it
An evil wizard has trapped you in the stairwell of his castle. Your only hope of escape is to run up all 100 steps to reach the top, and you can run one step per second. Unfortunately the wizard uses magic to lengthen the staircase by five steps per second. The new steps are inserted randomly between existing steps, so if you're lucky some of them might be beneath you and not ahead of you.


==A+B==
Can you escape, or are you doomed to run up an ever-lengthening staircase forever?


Input a number of the form 2^a 3^b
Write a program to simulate your escape attempt. How are you doing after ten minutes? For every second between 600 and 609 seconds inclusive print the number of steps behind you and the number still ahead of you.
<lang fractran>
2/3
</lang>
The output is 2^(a+b)


==Empty program==
If you escaped, run 10,000 tests and print the average time taken and the average final length of the staircase.


A list of no fractions does nothing, then immediately stops.
==header|Fermat==
<lang fermat>
<lang fractran></lang>
time_tot:=0; {we'll keep track of the total time and steps across all the trials}
steps_tot:=0;
!!('Seconds ','Steps behind ','Steps ahead');
for trial = 1 to 10 do
s_behind:=0; {initialise staircase and runner for this trial}
stair_len:=100;
time:=0;
while s_behind < stair_len do
s_behind:=s_behind + 1;
for wiz = 1 to 5 do
stair_len:=stair_len + 1; {evil wizard creates a step} {(mwaahahaha)}
if (Rand|stair_len) < s_behind then
s_behind:=s_behind + 1;
fi
od;
time:=time+1; {another second has passed}
if trial = 1 and 599<time and time<610 then
!!(time, ' ', s_behind, ' ',stair_len-s_behind)
fi;
od;
time_tot:=time_tot+time;
steps_tot:=steps_tot+stair_len;
od;


==Integer Sequence==
!!(time_tot/10000);
Given the number 1 as input the following program will, as its (3n-2)th step, produce the number 2^n.
!!(steps_tot/10000);</lang>
<lang fractran> 2/3, 9/2, 2/1</lang>
{{out}}<pre>
Seconds Steps behind Steps ahead
600 2102 998
601 2105 1000
602 2110 1000
603 2116 999
604 2121 999
605 2126 999
606 2131 999
607 2137 998
608 2142 998
609 2145 1000
29037 / 10000
29237 / 2000
</pre>
Seconds Steps behind Steps ahead
600 2125 975
601 2129 976
602 2132 978
603 2136 979
604 2142 978
605 2146 979
606 2151 979
607 2156 979
608 2162 978
609 2166 979
3697083 / 1250
3722083 / 250
</pre>


==Logical operations==
==header|FreeBASIC==
It's not so hard to code up all sixteen possible two-input logic gates, so here they are. The input is 2^a 3^b where a,b are zero or one and the output is 5^1 for true and 5^0 for false. Gates that return true when all their inputs are false additionally require the flag 11 to be set as input (ie 2^a*3^b*11)- any FRACTRAN program with the number 1 as input either stops without doing anything or loops forever.


<lang freebasic>
<lang fractran>
5/6, 1/2, 1/3 AND gate
randomize timer
5/6, 5/2, 5/3 OR gate
dim as uinteger steps_behind = 0, stairs_length = 100, seconds, j
1/22, 5/11 NOT gate (uses 11 as a halt flag, result of 2^a*11 is 5^not(a))
dim as uinteger seconds_tot, steps_tot
1/6, 5/2, 5/3 XOR gate
print "Seconds", "steps behind", "steps ahead"
1/66, 5/22, 5/33, 5/11 NAND gate (needs 11 flag)
for trial as uinteger = 1 to 10000 'We'll have the runner try this 10000 times
5/66, 1/22, 1/33, 5/11 NXOR gate (needs flag)
steps_behind = 0 'runner starts at the bottom
1/66, 1/22, 1/33, 5/11 NOR gate (needs flag)
seconds = 0 'reset time taken
stairs_length = 100 'Staircase has 100 steps
while steps_behind < stairs_length 'if the runner hasn't reached the top
steps_behind += 1 'go up one step
for j = 1 to 5 'The evil wizard conjures another five steps
if int(rnd*stairs_length) < steps_behind then steps_behind += 1
'there's a chance that a new step will be behind you
stairs_length += 1 'but either way the staircase is one step longer
next j
seconds += 1 'that all took one second
if trial = 1 and seconds >599 and seconds < 610 then print seconds, steps_behind, stairs_length - steps_behind
'for the first attempt, see how the runner is doing after ten minutes
wend
seconds_tot += seconds 'if the runner escaped, track the time taken and the length of the stairs
steps_tot += stairs_length
next trial


so much for all the commonly encountered ones, but there's still another eight to go. Most are obscure and of limited utility.
print "Average time taken: ";seconds_tot/10000; " seconds."

print "Average final staircase length: ";steps_tot/10000; " steps."
1/2, 1/3 ZERO gate, returns false regardless of its input
'if you noticed that last number is about 100*exp(5), that's no coincidence</lang>
1/6, 5/2, 1/3 "A and not B", true only if A is true and B is false
{{out}}<pre>
5/2, 1/3 A , returns the state of A regardless of B
Seconds steps behind steps ahead
600 2032 1068
1/6, 1/2, 5/3 "B and not A", true only if B is true and A is false
601 2038 1067
1/2, 5/3 B , returns the state of B regardless of A
602 2042 1068
1/66, 1/33, 5/11 "A or not B" (needs flag)
603 2045 1070
1/66, 1/22, 5/11 "B or not A" (needs flag)
5/66, 5/22, 5/33, 5/11 ONE gate, returns true regardless of its input, needs flag
604 2048 1072

605 2053 1072
NOT A and NOT B are omitted because the one-input NOT gate is already up there.
606 2055 1075
</lang>
607 2060 1075

608 2064 1076
==Sort three variables==
609 2068 1077
FRACTRAN's only data type is positive integers. Suppose (a,b,c) are the integers to be sorted. Give the following as input:
Average time taken: 2921.9457 seconds.
2^a 3^b 5^c
Average final staircase length: 14709.7285 steps.
<lang fractran>
</pre>
1001/30, 143/6, 143/10, 143/15, 13/2, 13/3, 13/5
</lang>
Returns 7^A 11^B 13^C where (A,B,C) are (a,b,c) in ascending order.

Latest revision as of 11:27, 28 November 2021

Some FRACTRAN programs in case we ever have a category for it

A+B

Input a number of the form 2^a 3^b <lang fractran> 2/3 </lang> The output is 2^(a+b)

Empty program

A list of no fractions does nothing, then immediately stops. <lang fractran></lang>

Integer Sequence

Given the number 1 as input the following program will, as its (3n-2)th step, produce the number 2^n. <lang fractran> 2/3, 9/2, 2/1</lang>

Logical operations

It's not so hard to code up all sixteen possible two-input logic gates, so here they are. The input is 2^a 3^b where a,b are zero or one and the output is 5^1 for true and 5^0 for false. Gates that return true when all their inputs are false additionally require the flag 11 to be set as input (ie 2^a*3^b*11)- any FRACTRAN program with the number 1 as input either stops without doing anything or loops forever.

<lang fractran> 5/6, 1/2, 1/3 AND gate 5/6, 5/2, 5/3 OR gate 1/22, 5/11 NOT gate (uses 11 as a halt flag, result of 2^a*11 is 5^not(a)) 1/6, 5/2, 5/3 XOR gate 1/66, 5/22, 5/33, 5/11 NAND gate (needs 11 flag) 5/66, 1/22, 1/33, 5/11 NXOR gate (needs flag) 1/66, 1/22, 1/33, 5/11 NOR gate (needs flag)

so much for all the commonly encountered ones, but there's still another eight to go. Most are obscure and of limited utility.

1/2, 1/3 ZERO gate, returns false regardless of its input 1/6, 5/2, 1/3 "A and not B", true only if A is true and B is false 5/2, 1/3 A , returns the state of A regardless of B 1/6, 1/2, 5/3 "B and not A", true only if B is true and A is false 1/2, 5/3 B , returns the state of B regardless of A 1/66, 1/33, 5/11 "A or not B" (needs flag) 1/66, 1/22, 5/11 "B or not A" (needs flag) 5/66, 5/22, 5/33, 5/11 ONE gate, returns true regardless of its input, needs flag

NOT A and NOT B are omitted because the one-input NOT gate is already up there. </lang>

Sort three variables

FRACTRAN's only data type is positive integers. Suppose (a,b,c) are the integers to be sorted. Give the following as input: 2^a 3^b 5^c <lang fractran> 1001/30, 143/6, 143/10, 143/15, 13/2, 13/3, 13/5 </lang> Returns 7^A 11^B 13^C where (A,B,C) are (a,b,c) in ascending order.

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