Flowers and berries

Mutagenesis

A sandbox for playing with algorithmic plant generation. You start with a simple plant species and create new species using random mutations and selective breeding.

Awards


Phyllotactical advantage
Presented by Cosmologicon

The Unintentional Pun: "growing plants in a 'sandbox' game" award
Presented by tnelsond

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Scores

Ratings (show detail)

Overall: 3.3
Fun: 2.5
Production: 3.7
Innovation: 3.8

Respondents: 24

Files

File Size Uploader Date
Mutagenesis-1.2.zipfinal
Version 1.2 Source
453.3 KB gcewing 2011/09/18 01:26
Screenshot5.png
Flowers and berries
118.7 KB gcewing 2011/09/17 11:29
Mutagenesis-1.1.zipfinal
Version 1.1 Source
276.8 KB gcewing 2011/09/17 11:28
Hoopplant.png
Hoop Plant
7.7 KB gcewing 2011/09/17 00:15
Screenshot4.png
More buttons!
82.2 KB gcewing 2011/09/16 12:11
Mutagenesis-1.0.zipfinal
Version 1.0 Source
216.5 KB gcewing 2011/09/16 12:09
Creeper.png
A creeper
56.0 KB gcewing 2011/09/16 08:23
Screenshot3.png
New-look buttons and catalogue area
59.7 KB gcewing 2011/09/15 13:10
Montage.png
Mutated plants
117.4 KB gcewing 2011/09/14 12:14
StartingPlant.png
Starting plant
16.4 KB gcewing 2011/09/14 12:07
Screenshot2.png
Initial plant with leaves
60.4 KB gcewing 2011/09/14 12:03
Screenshot1.png
Plant growth!
48.7 KB gcewing 2011/09/12 10:40

Diary Entries

Mutagenesis - Technical Notes

As promised earlier, here are some notes about what's going on inside Mutagenesis. This is mainly for the curious -- you don't have to know about any of this to play the game, although having some idea of what's behind it may help you to make a bit more sense of the outcomes.

DNA and its Interpretation

The DNA of each plant is an L-system (Lindenmayer system), which is a
kind of grammar. It consists of a collection of productions, each of
which has a left hand side and a right hand side. Here's an example
of the DNA for a simple plant:

1:    A --> wwwwB
2:    B --> [A][A]
3:    B --> [L][L]A
4:    L --> {llwrwrw}

The structure of a plant is represented by a string of characters. In
my system, upper case letters are nonterminal symbols, and lower case
letters and digits are terminal symbols. Some other characters such as
brackets and braces are also used, with meanings that will be described
below.

The seed of a new plant is the string "A". At each growth step, every
nonterminal symbol is simultaneously replaced according to a production.
If more than one production applies, one of them is chosen at random
for each replacement.

The first few steps of growth for the above DNA might look like
this:

  A
  wwwwB
  wwww[A][A]
  wwww[wwwwB][wwwwB]
  wwww[wwww[L][L]A][wwww[A][A]]
  wwww[wwww[{llwrwrw}][{llwrwrw}]wwwwB][wwww[wwwwB][wwwwB]]
 
To turn the string into a graphical representation, a scheme based on
turtle graphics is used. The turtle starts off at the root of the plant,
facing upwards. Terminal characters in the string are then interpreted
as a sequence of commands for the turtle:

  w - move forward a short distance and draw a line
  l - turn left by a predetermined angle
  r - turn right by a predetermined angle

The 'w' command currently always draws a brown line, representing a piece
of stem ('w' stands for 'wood'), and the turning angle for 'l' and 'w'
is fixed at 10 degrees.

Square brackets are used to enclose branches. When a branch is encountered,
a new turtle is created with the same initial state as the current one,
turned to a new angle, and used to interpret the characters inside the
brackets. Interpretation of the main string then resumes using the original
turtle.

A series of branches without intervening commands are automatically
distributed at increasing angles either side of the main axis, currently
at fixed 20 degree increments.

Curly braces represent filled shapes. The commands inside the braces are
interpreted by a new turtle, and the points that it traces out are used as
the control points of a Bezier curve. This curve is then mirrored twice
(left-right and forward-backward) and the resulting shape filled in.

In the above example, a filled shape is used to represent a leaf.

So we can paraphrase the meaning of this DNA as follows: A plant begins by growing
a piece of stem. The tip of the stem can then turn into either a new pair of
stems branching to either side, or a pair of leaves and another stem continuing
straight ahead. Each new stem develops in the same way as the original plant.

This simple plant is rather boring, since it as leaves but no flowers or
fruit. The full DNA of the initial plant used in the game is more complex,
and uses some additional commands. It looks like this:

1:    A --> wwwwB
2:    B --> [A][A]
3:    B --> [L][L]A
4:    B --> [C][C]
5:    C --> wwwwD
6:    D --> [C][C]
7:    D --> [L][L]C
8:    D --> E
9:    E --> [G][C]
10:   E --> [C][G]
11:   G --> wO
12:   G --> wwF
13:   L --> {7cllwrwrw}
14:   O --> 1c5do
15:   F --> 5b[P]S
16:   P --> {6clllwrw}
17:   S --> 3c6do

The new commands are:

    1-9     Establishes a parameter value. Which parameter is set depends on the
            next parameter-setting command encountered, as described below.
         
    c       Sets the colour used for filling shapes.
   
    d       Sets the diameter of circles.
   
    b       Sets the branch multiple (see below).
   
    o       Draws a filled circle with colour and diameter determined by the most
            recent 'c' and 'd' commands.

Parameter values corresond to colours as follows:

    1  red 
    2  orange 
    3  yellow 
    4  light green 
    5  light blue 
    6  white 
    7  dark green 
    8  dark blue 
    9  violet 

There are two examples of the 'o' (circle) command here. Production 14 uses it for
the centre of a flower, and production 17 uses it for a berry.

There are also two filled shapes. Production 13 is the leaf we saw earlier, with the
addition of a colour-setting command. Production 16 uses a similar but slightly
different shape with a different colour for a flower petal.

Production 15 generates a flower using another new feature: branch multiplication.
If a branch is encountered while a branch multiplier is in effect (having been set
by a previous 'b' command) the branch is repeated that many times, with the copies
distributed evenly around a full 360 degrees. Generating the flowers this way,
instead of using a separate branch for each petal, allows the number of petals and
the shape of the petals to mutate without disturbing the symmetry of the flower.

As well as the flowers and berries, there is another difference from the first
example: there are two nearly-identical copies of the first few productions. The
reason for this is to ensure that the plant grows for a couple of steps before
starting to produce flowers and berries, producing a more life-like distribution
of plant features.

Mutation

Mutating the DNA involves making a series of random decisions. The first is
whether to add a new production or change an existing production.

If a new production is being added, it is created by duplicating one of the
existing productions. Then there is a chance of replacing its left hand side
with a different nonterminal, either a new one or one already appearing
somewhere in the existing productions. If a new nonterminal is being added,
it is also inserted at a randomly chosen place in the right hand side of one
of the existing productions.

If an existing production is being mutated, either the left or right hand
side can be changed. The left hand side is mutated in a similar way to that
of a new production.

To mutate the right hand side of a production, a point in it is randomly
chosen. What happens next depends on the symbol found there:

- If it is '[' (the beginning of a branch), the whole branch may be
  duplicated or deleted.
 
- If it is ']' (the end of a branch), either a random nonterminal or a new
  branch containing a random nonterminal may be inserted after it.

- If it is a nonterminal, it may be replaced by another nonterminal or
  terminal, or deleted.

- If it is a terminal, it may be replaced by another terminal, a new
  terminal may be inserted before it, or it may be deleted. If it is a
  digit, the most likely mutation is to replace it by a different digit.

It's currently assumed that a separate production is used for each filled
shape, so that '{' and '}' only appear surrounding the whole right hand
side of a production, and that only terminal symbols occur inside the
braces. The initial DNA observes these constraints, and the mutation rules
preserve them.

The special treatment of nonterminal symbols is an attempt to prevent
unnatural-looking growth patterns from arising. In most plants, apart from
thickening of branches, growth only occurs at the tips. Only inserting
nonterminals at the ends of branches, and never after an existing
nonterminal, ensures that mutations can't cause growth to occur in the
middle of a branch. It also helps to limit the growth rate, so that the
number of symbols in the plant's structure doesn't explode too rapidly
at each step.

Cross-breeding

To cross-breed two sets of DNA, their lists of productions are laid out
side by side, a crossing-over procedure is applied to each pair, and the
result becomes the production list of the new plant. If one parent has
more productions than the other, the unpaired productions are appended
unchanged.

Crossing over a pair of productions involves choosing one of the left
hand sides at random, and crossing over the right hand side strings.

To cross over the right hand sides, they are first classified as either
filled shapes (surrounded by '{' and '}') or not. If they are both
filled shapes, their contents are crossed over and the result is a new
filled shape. If one is a filled shape and the other not, one of them is
chosen at random. If neither are filled shapes, they are crossed over as
described below.

To cross over a pair of strings, they are first divided into segments,
where each segment is either a complete branch (possibly containing
sub-branches) or a non-branch sequence of terminals. The segments are
then paired up.

If both members of a pair are branches, the contents of the two branches are
recursively crossed over. If a pair consists of a branch and a non-branch, one
of them is chosen at random.

If both members of a pair are non-branches, there is a chance that they
will be divided in two at randomly-chosen points and one piece chosen
from each half of each pair. The longer the segments, the greater the chance
that this will happen. (Long pieces of DNA are fragile and break easily!)

If there are more segments in one string than the other, the unpaired
segments are appended unchanged to the new string.

Further Reading

The Algorithmic Beauty of Plants, by Przemyslaw Prusinkiewicz and Aristid
Lindenmayer, available online at http://algorithmicbotany.org/papers/#abop

Most of my ideas for interpreting the L-systems using turtle graphics came
from here. The mutation and cross-breeding stuff I just made up as I went
along, though, so don't blame them for it.

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Mutagenesis - Day 8

Found a planty-looking font for the title screen, changed the background to dark green, and stomped a few last-minute bugs. Looking pretty good. Final final release made. I can stop drinking inadvisably large amounts of coffee now.

5 comments

Mutagenesis - Day 7

Lots of improvements. Flowers, berries and other such things are now possible, with colours, shapes and sizes all mutatable. Tweaked the mutation probabilities a bit in the hope of making unhelpful mutations less likely -- not sure how successful I've been with that. Pedigree of selected plant is displayed. Thumbnail data is saved with games so that they load faster.

I think I've pretty much got to the point I was hoping to reach. Time for a release!

Here's new starting plant, with some variations.

1 comment

Improved leaves

Leaves are now rendered with 4-fold symmetry, with the result that they no longer tend to turn into funnels when they mutate.

I'm also using bezier curves for their edges, although I'm not sure it's much of an advantage at the moment.

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Hoop Plant

Ladies and gentlemen, I present the first practical product from Grego Biolabs Inc. -- the Hoop Plant!

No longer do you have to spend money on expensive croquet hoops -- you can grow them yourself in your own back yard!

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Mutagenesis - Day 6

Cross-breeding is implemented. Also added a few sound effects to spice things up a bit.

Still to do:
  • Make the plants more interesting
  • Try to make mutations slightly less lethal
  • Give saved games a distinctive extension and magic number

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I made a creeper

It always branches to the left, and goes round in circles...

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Mutagenesis - Day 5

The user interface looks a bit nicer now, plants grow automatically, and there is a catalogue of the specimens you've created that you can select from.

Remaining to be done:
  • Cross-breeding
  • More plant features (flowers, fruit, colour variations)
  • Sounds
There are also a few problems that need attention. Repeated mutations seem to always end up producing a stunted plant or one that doesn't grow at all; I might need to bias the mutations a bit more towards adding symbols than deleting them.

The scheme I'm using to render leaves could also do with improvement. The initial hand-crafted leaf looks nicely leaf-shaped, but mutations of it almost invariably produce something with a flat end.

Current screen shot:



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Mutagenesis - Day 4

Plants can now have leaves. The leaf shapes can mutate

Realised that I wasn't going to gain anything from having the chromosomes paired, and got rid of that complication.

Totally rewrote the mutation code. It just seemed to need it.

The initial plant (hand-crafted) now looks like this:



And here are some mutations created from it:



As you can see, they tend to degenerate into a mess after a while. Not sure if that will turn out to be a bad thing or not. Hopefully when I get the cross-breeding part working it will be possible to breed better-looking specimens from what you have.

3 comments

Mutagenesis: Day 3

Didn't get anything done about rendering leaves, but did manage to get a basic mutation system working. It may need tweaking later.

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Decision made: Mutagenesis - Algorithmic plant generation

I'm trying something a bit different this time. Rather than a traditional game, this will be more of a sandbox for playing around with plant structures based on L-systems.

You will start off with one fairly simple species of plant. You have two ways of creating new species:
  1. Induce a random mutation
  2. Cross-breed two existing species
The DNA of a plant will consist of a set of chromosome pairs, where each chromosome is a production in an L-system. The pairing is irrelevant to the operation of the L-system, but it comes into play during cross-breeding, where a crossing-over procedure will be applied to each pair of chromosomes.

Mutations will consist of randomly adding or deleting symbols in the chromosomes, and maybe some other things such as duplicating entire branches or chromosomes to increase the overall complexity of the genome.

No predefined goal or fitness function is currently planned; it will be up to the player to set his own goal and work towards it, or just have fun playing around and seeing what comes out.

I'm also not currently intending to let the player directly see or edit the L-system, although I might add that later if I get time.

Day 1 Progress

Thought up the initial idea (after considering adapting my idea for More Criticals, which could have been stretched via the idea of radiation-induced mutation, but it wouldn't have fitted so well). Performed some initial research by reading the first few chapters of The Algorithmic Beauty of Plants. Came up with a plan of attack for the main implementation problems.

Day 2 Progress

Put together a basic game skeleton and started implementing the core idea. Got the basic L-system substitution mechanism working, and the beginnings of a rendering system. Can generate and display simple plants consisting entirely of woody stems (example below).

Plan for tomorrow: Need to get more visual elements into the rendering -- leaves, flowers, etc. Will experiment with encoding of filled polygons and colour variations.

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