From: Daniel Moore <yahivin@...>
Date: 2009-02-09T05:33:44+09:00
Subject: Re: Mathematical Image Generator (#191)

I'm still not doing a very good job of explaining this. One more
attempt, this time by a coding example.

CAUTION: Spoiler! If you want to generate random functions on your own
do not read further. This implements the function generation, not
anything specific to image generation.

Here is a class that will generate string representations of functions
given a specified depth. Feel free to use or modify this class in your
solutions.

class FunctionMaker
  def initialize()
    @functions = ["Math.sin(Math::PI * ?)", "Math.cos(Math::PI * ?)",
"(? + ?)/2", "? * ?", "(?) ** 3"]
  end

  # Create a string representation of a function at the given
  def create_function(depth)
    #if depth is 0, return either x or y randomly
    if depth == 0
      return "x" if rand > 0.5
      return "y"
    end

    #grab a random function from the list
    function = @functions[rand(@functions.length)]

    #for each instance of ? in the function, replace with a function
at the next shallower depth
    return function.gsub("?") { create_function(depth - 1) }
  end
end

Usage:
  fm = FunctionMaker.new
  fm.create_function(5)
=> "(Math.sin(Math::PI * ((Math.cos(Math::PI * y) + y * y)/2 + y * x *
y * y)/2)) ** 3"


On Sat, Feb 7, 2009 at 9:21 PM, Sean Mehan <sean@smo.uhi.ac.uk> wrote:
> And is this before or after collection?
>
> 2x + x + 5x = 8x, has one term of x at degree 1.
>
> 2x^2 -x + 4x^2 + x = 6x^2, has one term of x at degree 2 and none at
> degree 1....
>
>
> <quote who="Albert Schlef">
>> Di Mo wrote:
>>> My explanation of function depth is also somewhat confusing. If anyone
>>> sees what I'm getting at and wants to try and help me out with another
>>> explanation please do! Let me try again in the meantime:
>>
>> Does "depth" equal "the number of times 'x' (or 'y') appears in the
>> expression" ?