Blurring the truth, because lies tend to be prettier

I have been playing with my new RGB ants and this is my favourite image so far:

Apparently computerized ants bring out the arts student in me

I do though have to admit that I have rather cheated with this image. This is not pure output from the ants. When running my new code I quickly realised that the ants had a tendency to get into a temporary loop where they ran over a subset of cells for a period of time. This meant that the colour of these cells was very stark compared to the general blending which otherwise occurred. I solved this by applying a blender which compared each cell to its neighbours and if their difference was greater than some user-defined blur constant then it averaged the colour of the two cells and set both to that average. The blurring runs again and again until it carries out no more averaging. I have created a GIF to illustrate what effect this has:

At least it's a well blended murky grey...

As you can see, the blurring works but also tends to make the colour darker. I have listed the help of some computer scientists, and I will hopefully have a better blurring algorithm sorted out fairly soon. On the other hand the blurring tool has given me some ideas for other tools, like something to brighten up the image by adding a number to each RGB value of every cell or a contraster which increases the difference between coloured and non-coloured cells.

589793,

mathmo

Colours, colours everywhere; but not a drop of mink (153, 138, 119)

<Token apology>It has been a ridiculously long time since I last posted, but university.<\Token apology>

This post is a kind of confession, a confession that I am fairly idiotic. One of my friends at university was looking at this blog and noticed that when I was writing the 'colouring-in' code that I had my ants overwriting each other, i.e. that if a blue ant landed on a square which a green ant had last been to you would get blue. The conversation went something like:

"Y'know how <see above>, why did you write it to do that?"
"It was the only way I could think of to implement some sort of RGB colour scheme."
"Why don't you just get the ants to subtract one from the respective RGB colour of the cell they land on?"
"..." *I am so stealing that idea.*

I didn't explain it well above, but essentially RGB (RedGreenBlue) is a way of defining colour using triples (R,G,B) where 0  ≤ R,G,B ≤ 255. The size of the number determines how light or dark the contribution of that colour to the overall colour is. For example (0,0,0) is black, (255,255,255) is white and the colour of human flesh  is (255,125,64). Honestly, I'm not making this shit up.

I have now written the code for this, with the following premise:

1. All cells start with colour (255,255,255) (i.e. white).
2. When an ant lands on a cell the program sums the RGB values of that cell and if the number is even it turns left and if it is odd it turns right.
3. The colour of the cell changes by one in the respective colour, e.g. a blue ant would subtract one from the last number and a cyan ant would subtract one from the second and third colours.
4. If an ant encounters a wall it is moved one space backward and its direction randomly chosen. (I have kept the ability to make any shape of container for that ants.)

I have only played with this for a few minutes, but I thought I would share one of the initial images:

14159,

mathmo

Is this a blog post that I see before me?

This is a quick blog to share some awesome with you. I have spent the afternoon playing with my new macro, and have acquired a rather compulsive attitude towards 8-bit images.

Using Langton's Ants on Excel! Hmm, maybe it won't catch on.

Ah hem. You can expect the next few blog's to completely consist of 8-bit images I have stolen from the internet and coloured in using ants. And in case you have just joined the blog I am not pulverising a colony of ants from my back garden then using the resulting paste to defile a children's colouring-in book. They are digital ants. Which makes it okay. I think, I am yet to check this with the RSPCA. And so on to the images:

Do you get +1/2 life if you eat the first one?

It was when I was making the mushroom that I realised it would be much easier if I could use the same mechanism to colour in the edges as I do for selecting the colour of ants and adding the highlights. I also added the ability to make 'white' ants, which I needed for the face of the mushroom.

Pretty freakin' awesome

I got the pattern for this one off a blog. This is the coolest thing yet to come out of this project by a rather embarrassing amount. I have noticed a trend in my blog posts in that I very nearly never come back and do anything that I have put in a list. It is very probable that this list will suffer the same fate. This is a list of things I want to 8-bitanterize:

• A world map. Mercator's projection naturally, although I could be persuaded to go Gnomonic.
• Harry Potter.
• A famous painting.
• A random picture off of Facebook.

Those are in order of do-able but time consuming to impossible but I'll bloody well kill myself trying.

4159,

mathmo

Pikachu and Puns

"Hello project, it's been a while. I am sorry I haven't called (your macro) recently but things were getting a little intense and I needed a break; some time to play around with other programming languages y'know? There was this one I knew from university and things were going really great for a while. Then it started harping on about my soul and 'happiness', a little too religious for my liking. Anyway I am back for good now. mathmo"

Perhaps a little weird and probably highly confusing. There is a joke in there for the CompSci's, there is a joke in there for the Mathmo's, and there is a lot of confusion over the nature of my relationship with my computer for the rest of you. To put you at ease the above translates as "I have had to put my project aside for the last couple weeks to do university work, consisting of maths and programming in MatLab".

Moving swiftly onwards...

Pikachu, now with surprisingly small feet

Now, pick wisely:

• If you came here solely for a brightly coloured picture of Pikachu, I recommend you now head here.
• If you came here for an 8-bit technicolour image of Pikachu coloured in by 10 binary ants, keep scrolling.

At first this image seems like a fairly simple output. Just draw a black outline in Excel, then tell it what colour you want each section to be, and where you want each ant to start, and then you might as well tell it to put in highlights like the white's in Pikachu's eyes. Right. Simple.

I think my solution was pretty elegant; in my final version to get the above output you only needed to input:

Painting by letters, does this count as algebra?

Each lower-case letter is the starting point of an ant that has the colour indicated by the letter. Upper-case letters are the highlights, those colours are added on top of the ants' paths at the end of the computation. For instance the "y" indicates that a yellow ant should start from this position, and the "A" indicates that this cell should be coloured white at the end. I have also covered the possibility of you wanting to stack these, for example "yA" would be translated as "I want an ant with a yellow ant to start here and for this cell to be coloured white at the end". I have only included the primary and secondary hex colours (red, blue, green, yellow, pink, cyan) so far. The code for each colour is the first letter of the name of the colour; except for black and white, where black is "z" and white is "a". Damn you blue.

I also included the option for the user to alter the gradient of the colour. For example setting the gradient at 50 produced the block colours above, but setting it at 1 would give:

Nintendo came to regret zombie Pikachu

For this particular image the lower gradient doesn't really work, but sometimes it is quite a nice effect:

My next blog post will have many Pokeballs

In terms of the structure of the program I had to come up with a completely new set up. I completely scrapped the system where I stored the location of each ant each turn and then when it came to displaying only changing the colours where an ant stepped. Now each cell has a 'hit' counter, incrementing each time an ant lands on it and making the ant turn right if the counter is even and left if it is odd, as well as a variable which 'remembers' the colour of the last ant to land on that cell. The colours are only added when the result is outputted.

653,

mathmo

Colouring in: bored-student-in-the-early-hours-of-the-morning style

You remember the fun of colouring in don't you? A sheet of paper printed with some monochrome pattern was given to you by your parents to keep you quiet for a couple hours. You steadily coloured in each block with care and attention, pretending each one filled in was another area of Metropolis that had fallen to the pandemic... Oh, that was just me? Perhaps that goes some way to explaining why I am the sort of person who writes a programming blog at 3am.

Seeing as I am writing this at 3am I really should write about something. It would appear that I have written a very good introduction to a post about colouring in, which is particularly fortuitous as I have a very good program to write about that does exactly that.

What I have done is altered my last program so that instead of using a square box it uses any user inputted shape. To input a shape you first need to create a boundary of black cells, ensuring that it is closed, i.e. every black cell is touching at least two others horizontally, vertically or diagonally. You then need to set a spawn point by entering any characters in any one cell in the centre of your shape. In this rendition every ant is spawned at one cell for simplicity. So suppose I entered this:

A heart turns out to be an easy bit image.

Here the '<3' is my spawn point. If I then run my code with one ant it produces this:

The only thing cuter would be a kitten. I am not doing a kitten.

I am going to admit that it took me several runs to get this because the colours are still on random, but my romantic side refused to have anything put a red heart. Alright, pink. I'm not quite romantic enough to spend 30 minutes of non-sleeping for my computer to happen to pick brilliant crimson out of the sixteen million possible colours allowed by my code.

31,

mathmo

Art for maths sake

Sampling every 100, 50, 25, 10, 5, 1 steps.

This is the explanation for the images:

"First order of business was to fix my program from last post. Obviously the 22.8GB variable had to go. I managed to replace it with two 20KB variables, but in exchange for  that I have to spend a lot longer outputting. As per usual the program runs the entire simulation before outputting anything. When it gets to the visual output stage I have a counter which goes from 2 to 100000 with a step size of n. Every time the counter increments I change the colour of the cell that the ant is currently in to the colour it is meant to be at that turn according to the pre-processed simulation. That means that to get the full output I had to use a step size of 1, which is particularly processor-intensive but works. I then thought to myself "what would happen if I didn't use a step size of 1?". That resulted in the images above."

 I quite like the variety of styles in the images above, in particular:

• The sparsity of the 100-step image.
• The polka-dot of the 10-step image.
• The suspiciously like a colour-coded topological map 1-step image. (I wonder if I could alter Langton's Ant to produce a randomly generated landscape...)

If you have an opinion please comment below, I want to pursue these further and it would be great to have some idea of what looks best!

Oh and seeing as someone managed to solve my last number pattern (it was the differences of consecutive 5th powers) I have come up with a new one!

3,

mathmo

P.S. This is a bloody difficult one, I will be impressed if someone gets it!

My computer can't quite remember that much

I was planning to have a new post for you tonight, but some exceedingly bad programming on my part has scuppered that plan. More on that in a minute.

I have written a program that, if it was run on say your average supercomputer, would run very similarly to my initial multiple ant program except with a twist. When an ant lands on a coloured cell the cell won't revert to being white, it will instead turn a darker shade of the colour it currently is. To ensure this doesn't result in ants going in circles I have written it so that the cell alternates between being classed as 'coloured' or 'white' in the classical Langton's Ant sense.

I came up with this particular idea on a bus journey a couple days ago, when I realised that some of the patterns that have been cropping up are in their own way quite beautiful. I think this new iteration will result in some spectacular images.

A quick update on the developing maturity of my code:

• I have rediscovered For...Next loops. I am now saving about 5 minutes on each bit of code, as I don't need to go back at the end and find the counter=counter+1 that I have missed out. For...Next loops work by taking a number equal to some specified lower bound, running a piece of code with that number and then incrementing the number until the number equals some specified upper bound. Do While loops take a number and keep running the code while the number meets some condition, say being less than or equal to some specified upper bound. So they are virtually the same, except in a Do While loop you need to manually increment the number each time the code runs, which is a little bit tiresome when you have twenty of them.
• I have moved all of my colours into Hex, meaning I can get a much bigger range of colours. Read bigger as 300,000 times bigger.

And now finally we get to the reason I don't have anything juicy for you tonight...

The code I wrote tried to create a 22.8GB variable. Yes, a variable nearly 4 times larger than Skyrim. AND it was trying to create it in RAM. The thing is, I know exactly how to get around this as I did it that way in all of my previous code. I just happened to try something new and it has backfired spectacularly. The error was so big that instead of bringing up a basic error message Windows took control, fired off an error report to whomever those actually go to and restarted Excel. That has never happened to me before.

I will sort this all out tomorrow, by which time my computer will either have calmed down or comitted itself.

4651,

mathmo