Gravity
From Esolang
Gravity was invented by Safalra (Stephen Morley) on 4th August 2005, based on a idea from Isaac Newton. Gravity is very different from any other existing programming language. Although its behavior is well-defined and deterministic, the evolution of its space is in general non-computable, due to the nature of the differential equations that govern it.
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[edit] Introduction
The execution of a Gravity program consists of the simulation of the effects of gravity on a countably infinite number of point particles. The initial space configuration is an infinite two-dimensional grid of point particles positioned with one at every point (x,y), where x and y are integers, with all but a finite number of unit mass. When particles collide they are replaced according to a set of collision rules specified by the program. Input, output, and halting can happen only when collisions occur. It can be shown that a Turing machine cannot compute, in the general case, whether even a single collision will ever happen.
[edit] Examples
The language specification states that "comments are not permitted, but each program should ideally be accompanied by a mathematical paper offering a proof that the program behaves in the desired way." The examples below do not include proofs, but these can be found under "External resources".
[edit] Hello World program
The following code is a Gravity Hello, world! program. It outputs ASCII values corresponding to the phrase "Hello world", and then, assuming no input was provided, it halts.
(0,0) : 2 (1,1,1,1, 2) -> 3 : 72 (1,1,1,1, 3) -> 4 : 101 (1,1,1,1, 4) -> 5 : 108 (1,1,1,1, 5) -> 6 : 108 (1,1,1,1, 6) -> 7 : 111 (1,1,1,1, 7) -> 8 : 32 (1,1,1,1, 8) -> 9 : 119 (1,1,1,1, 9) -> 10 : 111 (1,1,1,1,10) -> 11 : 114 (1,1,1,1,11) -> 12 : 108 (1,1,1,1,12) -> # : 100
[edit] Cat program
The following code is a cat program. The encoding used can be any encoding that maps characters to a series of 3s and 4s (for example, mapping characters to their Unicode positions, and then turning 0 and 1 bits into 3s and 4s respectively).
(0,0) : 2 (1,1,1,1,2) -> # : (1,1,1,1,3) -> # : 3 (1,1,1,1,4) -> # : 4
[edit] Digital root program
The following code is the first few lines of a digital root program. The program works with the standard ASCII encoding of the digits 0 to 9. The full program is 113 lines long.
(0,0) : 2 (1,1,1,1, 2) -> # : (1,1,1,1,48) -> # : 48 (1,1,1,1,49) -> # : 49 (1,1,1,1,50) -> # : 50 (1,1,1,1,51) -> # : 51 (1,1,1,1,52) -> # : 52 (1,1,1,1,53) -> # : 53 (1,1,1,1,54) -> # : 54 (1,1,1,1,55) -> # : 55 (1,1,1,1,56) -> # : 56 (1,1,1,1,57) -> # : 57 (1,1,1,1,48) 48 -> 48 : (1,1,1,1,48) 49 -> 49 :
[edit] External resources
- Gravity (at Safalra's Website), with examples and proofs
