Random art

Insipired by Tsoding. Original paper here.

Premise

We can create an image by using a function that maps the (x, y) coordinates of the pixel to an (r, g, b) value. If we use the function f(x, y) -> (x, x, x) we get a greyscale image:

x and y are mapped to [-1, 1]. The results from the function are then scaled to map to [0,255] for each channel.

What if we could generate the functiion f randomly, then evaluate it on the (x, y) input !?

In the context of security, we can use for example an SSH key hash as the seed for RNG before generating the function, in effect, visualising the hash.

Some of my favourite images

These were generated by letting the grammar generate a function to a certain depth.

Depth3	Depth 6	Depth 1	Depth 4

All the images so far use this grammar given in the paper:

Extending the grammar

• ifgeq-then-else
• mod
• div
• sin
• cos
• exp

There's code to interpret these additional constructs, so it is possible to write ASTs by hand that use them. They haven't been added to the grammar. The grammar should be easily extendable, for example, the paper grammar is represented like so:

void grammar(){

    init_grammar(N_RULES);

    add_rule_to_grammar("E", RK_ENTRY);
    add_rule_to_grammar("A", RK_TERMINAL);
    add_normal_rule_to_grammar("C");

    init_branches(MAX_BRANCHES);

    assert(g.entry_point != NULL); // entry point must be defined
    assert(g.terminal_rule != NULL); // terminal rule must be defined

    add_branch_to_rule("E", branch_triple_rule("C", "C", "C", NK_E, 1));

    add_branch_to_rule("A", branch_no_rule(NK_NUMBER, 1.0/3.0));
    add_branch_to_rule("A", branch_no_rule(NK_X, 1.0/3.0));
    add_branch_to_rule("A", branch_no_rule(NK_Y, 1.0/3.0));

    add_branch_to_rule("C", branch_single_rule("A", 0.1));
    add_branch_to_rule("C", branch_double_rule("C", "C", NK_ADD, 0.45));
    add_branch_to_rule("C", branch_double_rule("C", "C", NK_MULT, 0.45));
}

These are some images produces from ASTs that implement these operators:

Depth 2	Depth 5	Depth 13
E(y,add(x, x) >= div(y, y),y)	Function too big to show here	Function too big to show here

Running

./randomart will start the program, prompting you for an input. Using a series of commands controls what it does.

By default, the program rendersn image from a randomly generated AST at depth 1. Typing enter runs with this default configuration:

$ ./randomart 
GRAMMAR: 
E ::= (C,C,C) [1.000000]
A ::= random number [-1 1] [0.333333] | x [0.333333] | y [0.333333]
C ::= A [0.100000] | add(C, C) [0.300000] | div(C, C) [0.300000] | sin(C) [0.300000]

> 
E(x,x,x)
nodes in AST: 4

Rendering image.....

> 

You can also type in a function which will be parsed and interpreted:

$ ./randomart 
GRAMMAR: 
E ::= (C,C,C) [1.000000]
A ::= random number [-1 1] [0.333333] | x [0.333333] | y [0.333333]
C ::= A [0.100000] | add(C, C) [0.300000] | div(C, C) [0.300000] | sin(C) [0.300000]

> E(sin(0.3), add(x,y), y)
Rendering image.....

> 

• depth n sets the depth
• seed n sets the seed
• quit quits the program

Note:

• Nesting depth is currently limited to 50.

Todo

• Make it such that when a rule is defined to be terminal, it is actually written as a terminal rule. Currently, it's easy to claim the rule is terminal, but make it non-terminal.
• Write grammar parser to make it easier to define any grammar in a text file
• Exploration