Background
At one of these afternoons we were together with the family and someone had this children card game "Dobble". After playing it for a while there was the idea that it would be an amazing idea to have the game with personalized pictures as christmas present. So I went to the web and quickly found an related question on stackoverflow, with a nice python example implementation already on github.
The game:
- On each card are O unique pictures (i.e. a card can't have 2 of the same picture)
- Given any 2 cards chosen from the deck, there is 1 and only 1 matching picture.
- Matching pictures may be scaled differently on different cards but that is only to make the game harder (i.e. a small tree still matches a larger tree)
- You can produce a deck of N cards with N images. N must be prime so there is an order O (also prime number) that satisfies: N = O² + O + 1. Eg if you want to have a deck with 30+ images you have to have 31 images and 5 images per card. 31 = 5² + 5 +1. So take care, the more cards you need the more images you need to have.
Number of Images and Cards:
You can produce a deck of N cards witch requires a number of N images as well. The order O of the system needs to be a prime! On the cards you can place O + 1 images. O must be prime so the total number of cards is: N = O² + O + 1 . Eg if you want to have a deck with 30+ images you have to have 31 images and 5 images per card. 31 = 5² + 5 +1. So you will also get 31 images.
How to run:
Place 31 images in "input_images"
Requirements:
You need the pillow package installed
pip install pillow
Than run:
python create_cards.py -d input_images_directory -o out_images_directory -O number_of_images_per_card
Make sure that the number of images per card matches: N = O² + O + 1 (O: number of images per card, N: number of cards). Otherwise you don't create a finite geometric plane.
You will get images like the examples in out_images like these:
Its tested with python 2.7 and order of 5 --> 31 cards. For other configs it might be neccessary to change the code in draw.py because it may create overlays etc. You will find the cards of the game in the out_images folder.
For those interested in the Geometry behind: https://de.wikipedia.org/wiki/Fano-Ebene Discussion on the combinatorics: link
References:
- With thanks to: Neil G. shared example code for for the question http://stackoverflow.com/questions/6240113/what-are-the-mathematical-computational-principles-behind-this-game
- there is also an version for block design on sage math: ftp://ftp.fu-berlin.de/unix/misc/sage/linux/64bit/index.html
- Forked and modified from: https://github.com/WRadigan/pySpot-It