Recursive Images and Fractals

Recursive images

One of the cool thing about graphs is they can link to themselves. The reason why this is a graph and not a quad tree (as most maps are) is to create recursive images.

Here we will see how to create a recursive image continuing from the getting started image. Let us create a recursive image where Mt. Tacoma is inside Seattle, and Seattle is inside Mt. Tacoma.



In [18]:

    
%pylab inline
import sys
import os
sys.path.insert(0,'..')
import graphmap
from graphmap.graphmap_main import GraphMap
from graphmap.memory_persistence import MemoryPersistence
from graphmap.graph_helpers import NodeLink









    



Populating the interactive namespace from numpy and matplotlib



In [19]:

    
G = GraphMap(MemoryPersistence())
seattle_skyline_image_url = 'https://upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Space_Needle002.jpg/640px-Space_Needle002.jpg'
mt_tacoma_image_url = 'https://upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Mount_Rainier_from_the_Silver_Queen_Peak.jpg/1024px-Mount_Rainier_from_the_Silver_Queen_Peak.jpg'
seattle_node_link = NodeLink('seattle')
mt_tacoma_node_link = NodeLink('tacoma')
G.create_node(root_node_link=seattle_node_link, image_value_link=seattle_skyline_image_url)
G.create_node(root_node_link=mt_tacoma_node_link, image_value_link=mt_tacoma_image_url)
insert_quad_key = '13'
created_node_link_result = G.connect_child(root_node_link=seattle_node_link,
                                    quad_key=insert_quad_key,
                                    child_node_link=mt_tacoma_node_link)
created_node_link = created_node_link_result.value
print(created_node_link_result)









    



Result(root@3lCis5Gi2okZxUJ3LPGD,0,)



In [20]:

    
plt.imshow(G.get_image_at_quad_key(created_node_link, 256, '').value)









    Out[20]:





<matplotlib.image.AxesImage at 0x9b15898>

Insert self

So far this has been same as the getting started example. Now to create a recursive graph, we will take the created node link and insert itself in the quad key '1333'.

Diagram

What we are trying to create is something like this



In [21]:

    
recursive_quad_key = '1333'
recursive_node_link_result = G.connect_child(root_node_link=created_node_link,
                                    quad_key=recursive_quad_key,
                                    child_node_link=created_node_link)
recursive_node_link = recursive_node_link_result.value
print(recursive_node_link_result)









    



Result(root@H2xtpwmXXfwbBc3xNkUt,0,)

Result

Thus we have created a recursive image. This contains an image of Seattle, which has image of Tacoma, which has the first image in it. If you zoom in you will see more details



In [22]:

    
plt.imshow(G.get_image_at_quad_key(recursive_node_link, 256, '').value)
plt.figure()
plt.imshow(G.get_image_at_quad_key(recursive_node_link, 256, '1').value)
plt.figure()
plt.imshow(G.get_image_at_quad_key(recursive_node_link, 256, '13').value)









    Out[22]:





<matplotlib.image.AxesImage at 0xac73cf8>

Fractals

Suppose we want to create an infinitely thin line. We could describe it this neat way

self = [ self , blue ]
       [ green, self ]

As it replaces self with definition of self it will look like this

The end product will be

This is an infinitely thin line between colors blue and green. You can keep zooming but never see a blunt edge. View it in KaiiMaps



In [ ]: