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Cascade Correlation Network


1. Cascade Correlation Network

You will need version 1.225, or later, of conx.py to run these experiments.

All of the neural networks we have looked at in this module have had static structures. That is, none of the models change the layers or connections during training. They have only adjusted weights (one could claim that setting a weight to zero effectively removes the incoming node from the network). We will now look at some models that do dynamically alter their architectures.

1.1. Incremental Network

Here is a little program that starts with a small hidden layer, and incrementally adds nodes to it as it needs them:

from pyrobot.brain.conx import *
net = Network()
net.addLayers(2, 1, 1)
net.setInputs( [[0, 0], [0, 1], [1, 0], [1, 1]])
net.setTargets([[0], [1], [1], [0]])
net.tolerance = .25
net.reportRate = 100
cont = 0
while True:
    net.train(250, cont = cont)
    if not net.complete:
        net.addLayerNode("hidden")
        cont = 1
    else:
        break
net.displayConnections()
net.interactive = 1
net.sweep()

Although this is a useful network growing process, it can be performed in a much better way. For example, if you added a node that removed as much error as possible, then you don't need to train the weights to that node any further; the new node is effectively a "feature detector" and you really only need to learn how to use it. That is the idea behind the Cascade Correlation Network.

2. Cascade Correlation Network class

This class, called CascorNetwork, has a special "candidate" layer of units from which it incrementally draws new nodes as new hidden layers. As new candidate units are recruited into the main network, the new unit's input weights are frozen. The idea is that the candidate nodes represent some feature detector, and is frozen from ever changing afterwards. This saves time in not having to retrain these weights.

Cascade-correlation has two distinct training phases. In the first phase, all connections incident on the output layer are trained to minimize error on the training set. Since only one layer of connections are being trained in this phase, any single layer neural network weight update formula could be used. The quickprop weight change formula is used because it often has convergence advantages over the normal backpropagation formula and the perceptron learning rule. However, since initially there are no hidden units in the cascade-correlation network, it is obvious that more will be required to learn most interesting problems than simply training the output weights. There are three ways the output training phase can end. The first possibility is that the error of the network has dropped below a certain goal threshold and training is done. The second possibility is that a maximum number of epochs have passed and we just give up. The third possibility is that no more progress is being made on training and the error of the network is still too high to stop. Output training stagnation is detected by keeping track how much the error changes each epoch and how many epochs have passed since there was last an appreciable change in the error. Appreciable is defined in terms of the outputChangeThreshold parameter. If the change threshold times the previous total sum squared error is less than the magnitude of the change in the TSS error the stagnation counter is reset. If a number of epochs have passed equal to the outputPatience parameter without any appreciable error change the output training phase has stagnated.

CascadeCorrelationExtensions

Let's take a look at an example of an incrementally-growing neural network. This is also included in the Pyrobot/examples subdirectory.

(See also TwoSpiralsProblem to see how hard this problem is.)

# pyrobot/examples/twospy.py
from pyrobot.brain.cascor import *
net = CascadeCorNet(2,1, patience = 12, maxOutputEpochs = 200, maxCandEpochs = 200)
net.maxRandom = 1.0
net.addCandidateLayer(8)
net.useFahlmanActivationFunction()
lines = open("twospiral.dat",'r').readlines()
inputs = [[float(num) for num in line.split()[:-1]] for line in lines]
inputs = Numeric.array(inputs)
targets = Numeric.array([[float(line.split()[-1])] for line in lines])
net.setInputs(inputs)
net.setTargets(targets)
net.tolerance = 0.4
net.outputEpsilon = 1.0/194.0
net.outputDecay = 0.0
net.candEpsilon = 100.0/194.0
net.candDecay = 0.0
net.candChangeThreshold = 0.03
net.outputChangeThreshold = 0.01
net.setSigmoid_prime_offset( 0.1)
net.outputMu = 2.0
net.candMu = 2.0
net.train(50)

Data file, pyrobot/examples/twospiral.dat:

 6.50000  0.00000     0.5
-6.50000 -0.00000     -0.5
 6.31380  1.25590     0.5
-6.31380 -1.25590     -0.5
 5.88973  2.43961     0.5
-5.88973 -2.43961     -0.5
 5.24865  3.50704     0.5
-5.24865 -3.50704     -0.5
 4.41941  4.41943     0.5
-4.41941 -4.41943     -0.5
 3.43758  5.14473     0.5
-3.43758 -5.14473     -0.5
 2.34392  5.65877     0.5
-2.34392 -5.65877     -0.5
 1.18272  5.94601     0.5
-1.18272 -5.94601     -0.5
-0.00002  6.00000     0.5
 0.00002 -6.00000     -0.5
-1.15837  5.82341     0.5
 1.15837 -5.82341     -0.5
-2.24829  5.42778     0.5
 2.24829 -5.42778     -0.5
-3.22928  4.83290     0.5
 3.22928 -4.83290     -0.5
-4.06589  4.06584     0.5
 4.06589 -4.06584     -0.5
-4.72900  3.15978     0.5
 4.72900 -3.15978     -0.5
-5.19684  2.15256     0.5
 5.19684 -2.15256     -0.5
-5.45563  1.08515     0.5
 5.45563 -1.08515     -0.5
-5.50000 -0.00004     0.5
 5.50000  0.00004     -0.5
-5.33301 -1.06085     0.5
 5.33301  1.06085     -0.5
-4.96584 -2.05696     0.5
 4.96584  2.05696     -0.5
-4.41716 -2.95151     0.5
 4.41716  2.95151     -0.5
-3.71228 -3.71234     0.5
 3.71228  3.71234     -0.5
-2.88198 -4.31328     0.5
 2.88198  4.31328     -0.5
-1.96120 -4.73490     0.5
 1.96120  4.73490     -0.5
-0.98759 -4.96524     0.5
 0.98759  4.96524     -0.5
 0.00006 -5.00000     0.5
-0.00006  5.00000     -0.5
 0.96331 -4.84262     0.5
-0.96331  4.84262     -0.5
 1.86564 -4.50389     0.5
-1.86564  4.50389     -0.5
 2.67373 -4.00141     0.5
-2.67373  4.00141     -0.5
 3.35880 -3.35871     0.5
-3.35880  3.35871     -0.5
 3.89755 -2.60418     0.5
-3.89755  2.60418     -0.5
 4.27297 -1.76985     0.5
-4.27297  1.76985     -0.5
 4.47485 -0.89004     0.5
-4.47485  0.89004     -0.5
 4.50000  0.00007     0.5
-4.50000 -0.00007     -0.5
 4.35222  0.86578     0.5
-4.35222 -0.86578     -0.5
 4.04195  1.67430     0.5
-4.04195 -1.67430     -0.5
 3.58567  2.39595     0.5
-3.58567 -2.39595     -0.5
 3.00515  3.00525     0.5
-3.00515 -3.00525     -0.5
 2.32639  3.48182     0.5
-2.32639 -3.48182     -0.5
 1.57850  3.81103     0.5
-1.57850 -3.81103     -0.5
 0.79248  3.98445     0.5
-0.79248 -3.98445     -0.5
-0.00007  4.00000     0.5
 0.00007 -4.00000     -0.5
-0.76824  3.86183     0.5
 0.76824 -3.86183     -0.5
-1.48297  3.58000     0.5
 1.48297 -3.58000     -0.5
-2.11817  3.16994     0.5
 2.11817 -3.16994     -0.5
-2.65170  2.65160     0.5
 2.65170 -2.65160     -0.5
-3.06609  2.04860     0.5
 3.06609 -2.04860     -0.5
-3.34909  1.38716     0.5
 3.34909 -1.38716     -0.5
-3.49406  0.69493     0.5
 3.49406 -0.69493     -0.5
-3.50000 -0.00008     0.5
 3.50000  0.00008     -0.5
-3.37143 -0.67070     0.5
 3.37143  0.67070     -0.5
-3.11806 -1.29163     0.5
 3.11806  1.29163     -0.5
-2.75420 -1.84039     0.5
 2.75420  1.84039     -0.5
-2.29804 -2.29815     0.5
 2.29804  2.29815     -0.5
-1.77082 -2.65035     0.5
 1.77082  2.65035     -0.5
-1.19581 -2.88715     0.5
 1.19581  2.88715     -0.5
-0.59739 -3.00367     0.5
 0.59739  3.00367     -0.5
 0.00008 -3.00000     0.5
-0.00008  3.00000     -0.5
 0.57315 -2.88104     0.5
-0.57315  2.88104     -0.5
 1.10029 -2.65612     0.5
-1.10029  2.65612     -0.5
 1.56260 -2.33847     0.5
-1.56260  2.33847     -0.5
 1.94460 -1.94449     0.5
-1.94460  1.94449     -0.5
 2.23462 -1.49303     0.5
-2.23462  1.49303     -0.5
 2.42521 -1.00447     0.5
-2.42521  1.00447     -0.5
 2.51328 -0.49985     0.5
-2.51328  0.49985     -0.5
 2.50000  0.00007     0.5
-2.50000 -0.00007     -0.5
 2.39065  0.47560     0.5
-2.39065 -0.47560     -0.5
 2.19419  0.90894     0.5
-2.19419 -0.90894     -0.5
 1.92273  1.28482     0.5
-1.92273 -1.28482     -0.5
 1.59094  1.59104     0.5
-1.59094 -1.59104     -0.5
 1.21525  1.81888     0.5
-1.21525 -1.81888     -0.5
 0.81314  1.96327     0.5
-0.81314 -1.96327     -0.5
 0.40231  2.02288     0.5
-0.40231 -2.02288     -0.5
-0.00007  2.00000     0.5
 0.00007 -2.00000     -0.5
-0.37805  1.90026     0.5
 0.37805 -1.90026     -0.5
-0.71759  1.73225     0.5
 0.71759 -1.73225     -0.5
-1.00702  1.50700     0.5
 1.00702 -1.50700     -0.5
-1.23748  1.23739     0.5
 1.23748 -1.23739     -0.5
-1.40314  0.93748     0.5
 1.40314 -0.93748     -0.5
-1.50133  0.62181     0.5
 1.50133 -0.62181     -0.5
-1.53249  0.30477     0.5
 1.53249 -0.30477     -0.5
-1.50000 -0.00006     0.5
 1.50000  0.00006     -0.5
-1.40987 -0.28049     0.5
 1.40987  0.28049     -0.5
-1.27031 -0.52624     0.5
 1.27031  0.52624     -0.5
-1.09128 -0.72923     0.5
 1.09128  0.72923     -0.5
-0.88385 -0.88392     0.5
 0.88385  0.88392     -0.5
-0.65970 -0.98740     0.5
 0.65970  0.98740     -0.5
-0.43048 -1.03938     0.5
 0.43048  1.03938     -0.5
-0.20724 -1.04209     0.5
 0.20724  1.04209     -0.5
 0.00004 -1.00000     0.5
-0.00004  1.00000     -0.5
 0.18293 -0.91948     0.5
-0.18293  0.91948     -0.5
 0.33488 -0.80838     0.5
-0.33488  0.80838     -0.5
 0.45143 -0.67555     0.5
-0.45143  0.67555     -0.5
 0.53035 -0.53031     0.5
-0.53035  0.53031     -0.5
 0.57165 -0.38193     0.5
-0.57165  0.38193     -0.5
 0.57744 -0.23915     0.5
-0.57744  0.23915     -0.5
 0.55170 -0.10971     0.5
-0.55170  0.10971     -0.5
 0.50000  0.00002     0.5
-0.50000 -0.00002     -0.5

A sample run. Notice that the network is saved after each hidden layer is created and trained:

Conx, version 1.225 (psyco enabled)
Conx using seed: 1156352143.06
Conx using seed: 113
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 49.3824 | Correct: 0.0722 | RMS Error: 0.5045
Final #    13 | TSS Error: 47.8712 | Correct: 0.0619 | RMS Error: 0.4967
   Saving network to 'cascor-00.net'...
Candidate phase ------------------------------------
Epoch:     39 | Candidate Epoch:      25 | Best score:  0.0991
Recruiting candidate: 1, correlation(s): [ 0.10196249]
1  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 47.6514 | Correct: 0.0412 | RMS Error: 0.4956
Final #    18 | TSS Error: 46.4749 | Correct: 0.2268 | RMS Error: 0.4894
   Saving network to 'cascor-01.net'...
Candidate phase ------------------------------------
Epoch:     85 | Candidate Epoch:      25 | Best score:  0.1194
Recruiting candidate: 3, correlation(s): [-0.12259556]
2  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 46.1827 | Correct: 0.2577 | RMS Error: 0.4879
Final #    19 | TSS Error: 44.4322 | Correct: 0.3402 | RMS Error: 0.4786
   Saving network to 'cascor-02.net'...
Candidate phase ------------------------------------
Epoch:    133 | Candidate Epoch:      25 | Best score:  0.1428
Epoch:    158 | Candidate Epoch:      50 | Best score:  0.1666
Recruiting candidate: 4, correlation(s): [-0.17551362]
3  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 43.9075 | Correct: 0.3402 | RMS Error: 0.4757
Epoch #    25 | TSS Error: 40.6093 | Correct: 0.4330 | RMS Error: 0.4575
Final #    31 | TSS Error: 40.5388 | Correct: 0.4227 | RMS Error: 0.4571
   Saving network to 'cascor-03.net'...
Candidate phase ------------------------------------
Epoch:    230 | Candidate Epoch:      25 | Best score:  0.1520
Epoch:    255 | Candidate Epoch:      50 | Best score:  0.1810
Recruiting candidate: 1, correlation(s): [-0.18949365]
4  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 40.0594 | Correct: 0.4330 | RMS Error: 0.4544
Epoch #    25 | TSS Error: 37.2836 | Correct: 0.5052 | RMS Error: 0.4384
Final #    28 | TSS Error: 37.2552 | Correct: 0.4948 | RMS Error: 0.4382
   Saving network to 'cascor-04.net'...
Candidate phase ------------------------------------
Epoch:    331 | Candidate Epoch:      25 | Best score:  0.1916
Epoch:    356 | Candidate Epoch:      50 | Best score:  0.2231
Epoch:    381 | Candidate Epoch:      75 | Best score:  0.2374
Recruiting candidate: 5, correlation(s): [ 0.24960197]
5  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 36.5320 | Correct: 0.5258 | RMS Error: 0.4339
Epoch #    25 | TSS Error: 30.9592 | Correct: 0.6392 | RMS Error: 0.3995
Final #    43 | TSS Error: 30.6571 | Correct: 0.6392 | RMS Error: 0.3975
   Saving network to 'cascor-05.net'...
Candidate phase ------------------------------------
Epoch:    464 | Candidate Epoch:      25 | Best score:  0.1849
Epoch:    489 | Candidate Epoch:      50 | Best score:  0.1971
Recruiting candidate: 0, correlation(s): [ 0.20292907]
6  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 30.2783 | Correct: 0.6598 | RMS Error: 0.3951
Epoch #    25 | TSS Error: 27.7280 | Correct: 0.6598 | RMS Error: 0.3781
Final #    36 | TSS Error: 27.6303 | Correct: 0.6701 | RMS Error: 0.3774
   Saving network to 'cascor-06.net'...
Candidate phase ------------------------------------
Epoch:    551 | Candidate Epoch:      25 | Best score:  0.1292
Epoch:    576 | Candidate Epoch:      50 | Best score:  0.1688
Epoch:    601 | Candidate Epoch:      75 | Best score:  0.1859
Recruiting candidate: 1, correlation(s): [-0.1972709]
7  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 27.2880 | Correct: 0.6598 | RMS Error: 0.3750
Epoch #    25 | TSS Error: 25.2114 | Correct: 0.6701 | RMS Error: 0.3605
Epoch #    50 | TSS Error: 24.5610 | Correct: 0.6804 | RMS Error: 0.3558
Final #    51 | TSS Error: 24.5797 | Correct: 0.6701 | RMS Error: 0.3559
   Saving network to 'cascor-07.net'...
Candidate phase ------------------------------------
Epoch:    692 | Candidate Epoch:      25 | Best score:  0.1390
Recruiting candidate: 2, correlation(s): [-0.14828391]
8  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 24.4173 | Correct: 0.6701 | RMS Error: 0.3548
Epoch #    25 | TSS Error: 23.0971 | Correct: 0.7010 | RMS Error: 0.3450
Final #    40 | TSS Error: 22.9527 | Correct: 0.7010 | RMS Error: 0.3440
   Saving network to 'cascor-08.net'...
Candidate phase ------------------------------------
Epoch:    774 | Candidate Epoch:      25 | Best score:  0.1414
Epoch:    799 | Candidate Epoch:      50 | Best score:  0.1794
Epoch:    824 | Candidate Epoch:      75 | Best score:  0.2044
Epoch:    849 | Candidate Epoch:     100 | Best score:  0.2204
Epoch:    874 | Candidate Epoch:     125 | Best score:  0.2383
Recruiting candidate: 0, correlation(s): [-0.24205678]
9  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 22.4492 | Correct: 0.7010 | RMS Error: 0.3402
Epoch #    25 | TSS Error: 18.0696 | Correct: 0.7938 | RMS Error: 0.3052
Final #    46 | TSS Error: 17.7494 | Correct: 0.7835 | RMS Error: 0.3025
   Saving network to 'cascor-09.net'...
Candidate phase ------------------------------------
Epoch:    950 | Candidate Epoch:      25 | Best score:  0.1395
Epoch:    975 | Candidate Epoch:      50 | Best score:  0.2167
Epoch:   1000 | Candidate Epoch:      75 | Best score:  0.2436
Recruiting candidate: 1, correlation(s): [ 0.25960197]
10  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 17.4222 | Correct: 0.7938 | RMS Error: 0.2997
Epoch #    25 | TSS Error: 15.1816 | Correct: 0.7938 | RMS Error: 0.2797
Final #    43 | TSS Error: 14.9903 | Correct: 0.7732 | RMS Error: 0.2780
   Saving network to 'cascor-10.net'...
Candidate phase ------------------------------------
Epoch:   1088 | Candidate Epoch:      25 | Best score:  0.1788
Epoch:   1113 | Candidate Epoch:      50 | Best score:  0.2546
Epoch:   1138 | Candidate Epoch:      75 | Best score:  0.3313
Epoch:   1163 | Candidate Epoch:     100 | Best score:  0.3693
Epoch:   1188 | Candidate Epoch:     125 | Best score:  0.4090
Epoch:   1213 | Candidate Epoch:     150 | Best score:  0.4385
Epoch:   1238 | Candidate Epoch:     175 | Best score:  0.4665
Recruiting candidate: 4, correlation(s): [ 0.47423286]
11  Hidden nodes
Output phase    ------------------------------------
Epoch #     0 | TSS Error: 13.6599 | Correct: 0.8247 | RMS Error: 0.2654
Epoch #    25 | TSS Error: 7.7976 | Correct: 0.8866 | RMS Error: 0.2005
Epoch #    50 | TSS Error: 5.7311 | Correct: 0.9485 | RMS Error: 0.1719
Epoch #    75 | TSS Error: 4.3302 | Correct: 0.9691 | RMS Error: 0.1494
Epoch #   100 | TSS Error: 3.3293 | Correct: 0.9691 | RMS Error: 0.1310
Epoch #   125 | TSS Error: 2.6684 | Correct: 0.9691 | RMS Error: 0.1173
Final #   148 | TSS Error: 1.9784 | Correct: 1.0000 | RMS Error: 0.1010
   Saving network to 'cascor-11.net'...
Total epochs: 1392

To test each saved network on the two spirals problem:

# pyrobot/examples/plot.py
import sys, re
from pyrobot.brain.conx import *
import pyrobot.system as system

def frange(start, stop, step):
    x = start
    while x <= stop:
        yield x
        x += step

pattern = sys.argv[1]
current = 0 # start
char = "?"
match = re.search(re.escape(char) + "+", pattern)
filenames = []
if match:
    fstring = "%%0%dd" % len(match.group())
    filename = pattern[:match.start()] + \
               fstring % current + \
               pattern[match.end():]
    while system.file_exists(filename):
        filenames.append(filename)
        current += 1
        fstring = "%%0%dd" % len(match.group())
        filename = pattern[:match.start()] + \
                   fstring % current + \
                   pattern[match.end():]
else:
    filenames.append(pattern)
s = ["-1.0","-0.9","-0.8","-0.7","-0.6","-0.5","-0.4","-0.3","-0.2","-0.1","-0.0",
     "+0.0","+0.1","+0.2","+0.3","+0.4","+0.5","+0.6","+0.7","+0.8","+0.9","+1.0"]
p = "abcde-#@(0o.1234+67890"
for filename in filenames:
    if 1:
        print filename, "..."
        net = loadNetworkFromFile(filename, mode = "conx")
        net.useFahlmanActivationFunction()
        net.setSigmoid_prime_offset( 0.1)    
        net["candidate"].active = 0
        for y in frange(-6.5, 6.5, .5):
            line = ""
            for x in frange(-6.5, 6.5, .2):
                out = net.propagate(input = [x, y])
                line += p[s.index(str("%+2.1f" % out["output"][0]))]
            print line

and run it like:

python plot.py "cascor-??.net"

This might produce something like:

Conx, version 1.226 (psyco enabled)
cascor-00.net ...
Conx using seed: 1156360775.01
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000oooooooooooooooooooooo
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
ooooooooooooooooooooooooooooooooo................................
.................................................................
.................................................................
.................................................................
.................................................................
.......................111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
cascor-01.net ...
Conx using seed: 1156359150.92
((((((((((((((((((((((((((((((((((((((((((@@@@@@@@@@@@@@@@@@@@@@@
(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((
(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((
000000(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((
0000000000000000000000000000000000000000000000000000(((((((((((((
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
oooooooooooooooooooooooooooooooooooooo000000000000000000000000000
...........oooooooooooooooooooooooooooooooooooooooooooooooooooooo
.........................................................oooooooo
111111111111111111111111111111...................................
11111111111111111111111111111111111111111111111111111111111111111
0000((((((((((011111111111111111111111111111111111111111111111111
00000000000000000000000000000000011111111111111111111111111111111
00000000000000000000000000000000000000000000000000012222222222111
00000000000000000000000000000000000000000000000000000000000000000
oooooooooooooooooooooooooooooooooooo00000000000000000000000000000
.........oooooooooooooooooooooooooooooooooooooooooooooooooooooooo
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cascor-02.net ...
Conx using seed: 1156322527.82
######@@@@@@@@@@@@@@@@@@@((((((((((((((00000(@#####@@@@@@@@@@@@@@
##@@@@@@@@@@@@@@@@@@@((((((((((((((000000000(@@@@@@@@@@@@@@@@@@@@
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@@@@@@@((((((((((((((0000000000000ooooo..o0@@@@@@@@@(((((((((((((
@@@((((((((((((((000000000000oooooo......o(@@@@@((((((((((((((000
((((((((((((0000000000000ooooo......1111.0(((((((((((((((00000000
((((((((000000000000oooooo......11111111o((((((((((((000000000000
(((0000000000000oooooo.....11111111111110(((((((0000000000000oooo
00000000000oooooo......1111111111112221.0(((000000000000oooooo...
0000000oooooo.....1111111111111222222210000000000000ooooo......11
00oooooo......111111111111222222222222.00000000oooooo......111111
((((((((000000011111112222222222222221o0000ooooo......11111111111
((((000000000000oooooo......o(@@(2332.oooooo......111111111111222
000000000000oooooo.....1111.0(((((((((((((((000000011111112222222
0000000oooooo......11111111o((((((((((((000000000000oooooo......1
000oooooo.....11111111111110(((((((0000000000000ooooo......111111
oooo......1111111111112221o0(((000000000000oooooo......1111111111
.....1111111111111222222210000000000000ooooo......111111111111122
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1111111112222222222222221o0000oooooo.....111111111111122222222222
111122222222222222333332.oooooo......1111111111112222222222222233
222222222222223333333331.oo.....111111111111122222222222222333333
222222222233333333333321....1111111111112222222222222233333333333
22222333333333333333331111111111111122222222222222333333333333333
23333333333333333333321111111112222222222222233333333333333333334
33333333333333344444321111122222222222222333333333333333333344444
cascor-03.net ...
Conx using seed: 1156308349.27
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000
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00000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000oo..1o000000000000000000000000000
00000000000000000000o..122334444444442000000000000000000000000000
############@@(34444444444444444444440000000000000000000000000000
@@(00o..111111111111111111111####4444000000000000000000000oo.1123
11111111111111111111111111111#####################@23344444444444
1111111111111111111111111111(#########@@((0oo.1111111111111111111
1111111111111111111111111111.0oo..1111111111111111111111111111111
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11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111
cascor-04.net ...
Conx using seed: 1156369488.24
(((((((((@@@@@@@@@@@(0.111....oooo00000000((((((((@@@@@@@@@@@@###
0((((((((((@@@@@@@@@@@(o11111....oooo0000000((((((((@@@@@@@@@@@@@
0000(((((((((@@@@@@@@@@@(o11111....oooo000000(((((((((@@@@@@@@@@@
000000(((((((((@@@@@@@@@@@0.11111....oooo000000(((((((((@@@@@@@@@
00000000((((((((((@@@@@@@@@(0111111....ooo0000000((((((((((@@@@@@
oo00000000((((((((((@@@@@@@@@(o1111111...oo000000000(((((((((@@@@
oooo000000000(((((((((@@@@@@@@@(o1111111..oooo00000000(((((((((@@
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1....oooo00000000((((((((((@@@@@@@(0111111....oooo00000000(((((((
111....oooo00000000((((((((((@@@@@@@(o111111....oooo000000000((((
111111....ooo000000000(((((((((((((13.(0.111111....oooo00000000((
11111111....oooo00000ooo.1144444444443@@(01111111....oooo00000000
@@@@#########@@2333333344+++++++++++4@@@@@(o1111111....oooo000000
((000ooooooo00000000o23333333---#4+++@@@@@@@(.11111111.......1112
1111111....oooo0000000.233333#-----------##@@@@@@@(33444444444333
211111111....oooo00000001233@##########00o...11111....oooo0000000
22211111111....oooo000000o12o@02222222222222111111111...oooo00000
22222111111111....oooo000000.23333333222222222211111111....oooo00
2222222211111111....oooo000000123333333222222222211111111....oooo
322222222211111111....ooo000000o133333333322222222211111111....oo
33322222222211111111....oo0000000.2333333333222222222111111111...
33333222222222111111111..ooo0000000.2333333333222222222211111111.
333333322222222221111111...oooo0000001233333333322222222221111111
3333333333222222222111111....oooo00000o13333333333322222222211111
333333333333222222222111111....oooo00000.233333333333222222222111
43333333333333222222221111111....oooo00000.2333333333332222222222
44443333333333332222222211111111....oooo000o123333333333322222222
cascor-05.net ...
Conx using seed: 1156377406.14
-------------#################@@@@@@@@@@@((((@##########@@@@@@@@@
-------#################@@@@@@@@@@@(((((((((@#####@@@@@@@@@@@((((
-####################@@@@@@@(((((((((0000000@@@@@@@@@@@((((((((00
###############@@@@@@@@@@((((((0000000ooooo(@@@@@((((((((0000000o
#########@@@@@@@@@@@(((((((00000ooo....111o((((((((0000000oooo...
###@@@@@@@@@@@((((((((0000000o..11111111210((0000000oooo...111111
@@@@@@@@((((((((0000000oooo...1111222222210000ooo....111111122221
@@((((((((0000000oooo...11111111222233332.o....11111112222222210@
((((0000000ooo....111111111.0@####133333211111112222222222210@###
00000ooo....11111112222110@#########@4432222222222333322.0@@#####
oo....11111112222222210@##########@444#12222333333332.(@@@#@@@@@@
11111112222222222210@@@@@@(+++++++++++###@33333332.(@@@@@@@@@@@@(
@@@@@@@(((((00142.0000o++++++++++++++@######.22.(@@@@@@@@@(((((((
(00.1111222222333333334444444----++++#######@@@@@@@@((((((0000o11
222222223333333332o((o4444443--------------.1111o(#01122222333333
223333333333332o(@@@@@@@3444-----------233333310(((((((((((000000
333333343332o(@@@@@@@@((((04###34444444444310((((((((0000000oooo.
444444331o((@@@@((((((((((@##34444444443100((((0000000oooo...1111
4444310(((((((((((0000000(@@@@@0444431o000000000oooo...1111111222
4310((((((((0000000oooo.o(@@@@((((00000000ooo....1111111222222223
o0((((0000000oooo...11110(((((((0000ooo....1111111222222223333333
0000000ooo....11111112210(00000000oo.1111111222222223333333333344
0ooo....111111122222222.000oooo...1111122222223333333333344444444
..111111122222222333332.....1111111222222333333333344444444444444
11122222222333333333331111111222222222333333344444444444444444444
22222333333333334444432222222223333333333344444444444444444++++++
33333333334444444444322223333333333344444444444444444++++++++++++
cascor-06.net ...
Conx using seed: 1156332439.34
-##############@@@@@(00(@###########@@@@@@@@@##########@@@@@@@(((
############@@@@@@@@((0oo0(@#####@@@@@@@@(((@#######@@@@@@@((((((
#########@@@@@@@@(((((00.11o(@@@@@@@@@((((((@####@@@@@@@((((((000
######@@@@@@@@((((((0000o.12210(@@@((((((0(@@#@@@@@@@((((((00000o
###@@@@@@@@((((((00000oo..112331o0((((0000(@@@@@@@@(((((00000ooo.
#@@@@@@@((((((00000oo...1111223332.00000o0(@@@@@(((((00000ooo..11
@@@@@((((((00000ooo..1111122223344431...o0(@((((((000000oo..11111
@@((((((00000ooo..1111122222222234444321.o0((((000000oo..11111.o0
(((((00000ooo..1111122222222o#----@444444331o00000oo...1111.0((((
((00000ooo..11111222222221#-------###++44444321.....111.o0(((((((
0000ooo..11111222222221(-------####+++#4444444421111.o0(((((((000
0ooo..11111222222221.#-####+++++++++++---#4+++431.0(((((((((00000
#####@@@@@@((0o4330###@++++++++++++++#----##(1o0(((((((((00000oo.
@((00oo.1111222222333444+++++----++++-----###@@@((((((0000o..1122
oo..111112222222221.0244++++4--------------34441@@#.1223333334444
.111112222222221o0@#---#4+++-----------4444+4o0((((((((00000oo...
111122222221.o0000(########4---4444+++++++20((((((((00000oo...111
122222221.o000ooooo0(@#####--444+++++++40((((((((00000oo...111112
222221o0000ooo..11111.0@@######3++++4.((((((((00000oo...111112222
21.o00000oo..11111122221.o0(@####@(((((((((00000oo...111112222223
000000oo..111111222222321.ooo0@###@@((((00000oo...111112222223333
000oo...11111222223333321.11111o(@@@((0000ooo..111112222223333333
oo...1111122222333333332111122221.0@@(00oo..111112222223333333344
..11111222222333333343321222222333210((0o.11112222223333333344444
11112222223333333444432222223333333332.00o11222223333333344444444
12222223333333444444432223333333344444321..1223333333344444444444
22223333333444444444433333333344444444444321123333344444444444444
cascor-07.net ...
Conx using seed: 1156332952.92
###########@@@@@@@@((0o0@@#######@@@@@@@@@((@@########@@@@@@@@(((
#########@@@@@@@@(((((0..0(@@##@@@@@@@@(((((@######@@@@@@@@@(((((
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####@@@@@@@@((((((000000o.12210((@(((((((0(@@#@@@@@@@@@((((((0000
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@@@@@@@((((((000000ooo..1111223332.0000000@@@@@@@@((((((000000oo.
@@@@@((((((000000oo...111112222344321ooo0(@@@@@(((((((00000ooo...
@@(((((((00000ooo..111111222222234444321o0(((((((((000000ooooo0((
((((((000000oo...111112222220-----@44444442.0((((00000ooooo0(@@@@
((((00000ooo..111111222211----------#+++++++41o00000ooo00(@@@@@((
(000000oo...1111112211.@-----------+++-4++++++43.oo00((((0000oo..
0000ooo...111111211.0-----#+++++++++++---#+++++4.ooo00000ooo...11
#########@@@@(0332(####++++++++++++++------#021.o000000ooo..11111
#@@(((000oo...11111224+++++++----++++-------#((00000ooo..11122233
000000oo...111111.o0(14++++++--------------44442(@@12333344444444
000ooo...11111...o#-----4+++-----------4+++++1o00(000000ooo...111
0oo..1111222211..o@#------#+---+++++++++++3o00((000000ooo..111111
12233333211...11111.0#-------4++++++++++00((((000000oo...11111222
3333321.....1111122221o(#######3+++++1((((((00000ooo..11111122222
3221.....1111112222222221.0(@####@(((((((000000oo...1111122222223
.ooo...1111122222223333321...0(@##@((((00000ooo..1111112222223333
oo..111111222222333333331111111o(@@@((0000oo...111111222222333333
..1111112222223333333332111122221.0(@(00oo...11111222222333333333
1111122222233333333343321222222232210((0o.11111122222233333333444
11122222233333333444432222222333333332o00o11122222233333333344444
22222233333333344444432222233333333443321oo1222223333333344444444
2222333333334444444433223333333334444444331.122333333334444444444
cascor-08.net ...
Conx using seed: 1156336341.21
-----#############@@@(0(@@##@@@@@@@(((((00000(@@@@@(((((0000oo...
-----############@@@@@(000(@@@@@@@@(((((0000(@@@@@(((((00000oo..1
----#############@@@@@@(0o.0(@@@@@(((((00000@@@@@(((((00000oo..11
---#############@@@@@@(((0o11o0(((((((00000(@@@@@(((((0000oo..111
##############@@@@@@@(((((00111.0((((00000(@@@@@(((((0000oo..1111
@@@@@@@@@@@@@(((((((((((0000o.2221o0000000(@@@@(((((0000ooo..1111
@(((((00000ooo....111111111111122321.0000(@@@@(((((00000oo..11111
(((((0000oo..11111222222333333223333321o00((@(((((00000oo...1.o0(
((((0000oo...111122222333333o-----#4+4324410((((((0000ooooo0(@@@@
(((0000ooo..11112222223321-----------+++++++4o0000000000(@@@@@@@(
((00000oo..111122222221(-----------+++-++++++++20000((@@@(((0000o
((0000oo..111112221.0------+++++++++++----++++++0(0(((((((00000oo
#########@@@((o433#####++++++++++++++-------.432.0((((((00000ooo.
#@((00oo000000000ooo14+++++++----++++-------#0...111111111..11223
oo...111112222221o(@#o+++++++--------------44444@@#.2233344444444
o..111112222222121------++++-----------++++++1o0(((00000oo..11112
..1111222333221111(--------+---+++++++++++20(((((((0000oo..111112
22333333321111111111.#-------+++++++++++0(@@((((((0000oo...111122
3333321.....111122222210##(@#-#4+++++.@@@@@@(((((0000ooo..1111222
321.o0ooo..111112222232211.0(@@@@@((@@@@@@((((((00000oo..11112222
000000oo..1111122222333321111o0(@((0000000000000oooo...1111122222
(0000oo...111122222333321111111.0(((o.111122222222222333333333333
00000oo..1111222223333321111122221o000112222233333334444444444444
0000oo..1111222223333321111122222221.00.12223333334444444444444++
000oo..11111222223333311111222223333321o.123333334444444444444+++
00oo..1111122222333332111122222333333332111233333444444444444++++
0ooo..1111222223333321111122222333333344332123334444444444444++++
cascor-09.net ...
Conx using seed: 1156361953.69
---------##########@@0o0#-----#@(0000000(((((@###################
-----------#@@@@@@@@@@(o.o#----#@(0ooo000000(@@@@@@@#############
------------#@@@@@@@@@@(011.##--##(0......o0(@@@@@@@@@@@@@@@@@@##
--------------#@(((((((((0.22.#####@0.111110((((((((((@@@@@@@@@@@
---------------#@(00000(((0o122.#####@o12210000000(((((((((((((((
#############@(0ooooooo00000o1233.####@(..@#(0000000000000000((((
#######@01222222222211111111..12333.@##@@####@(o.....oooooo00000(
########@0123333333332222222211123444.@@#######@0111111111..o0(@#
@@@@@@@@@@(.2333333333333322o------44443442@####@(.1222111.0@####
(((@@@@@@@@(01344444443321-----------+++++++4@####@01221o(@######
((((((((((((((.24444432o-----------+++-4+++++++1####(00((@@@@@@@@
0000000000((((0023321------+++++++++++----++++++@###@((00((((((((
#############@2++4#####++++++++++++++-------@+32(###@(00000000000
@((000000000(((((((002+++++++----++++-------(11222222211111111122
111111111111234442(@-3+++++++--------------44444#--(3444444444444
222222222112234443------++++-----------++++++0(@@(112222111111111
3333333332211244440-------#+---+++++++++++.(@#####(o2222222222222
444444432.0((01344443#-------+++++++++++0(@@#######@0123333333322
+444431o000(((0o2344443(##@####++++++.((@@@@@@@@@@@@@(o2333333333
44321.oo00000000013444444433o###@(000((((((((@@@@@@@@@(0134444444
2211111......ooooo.23444433443o@@@(0oo00000000((((((((((013444444
222221111111111111111243oo234444o@@(0.11111.......123444444444444
322222222222222211111110((0.344444o((0.122211111234++++++++++++++
3333333333332222222222100000o1344444o((o122222222234+++++++++++++
44433333333333333333321.oooooo1244++44o001233333333334+++++++++++
4444444444444433333332111111...1234++++4.o.233333333334++++++++++
444444444444444444443222221111111234+++++41.1334444444444++++++++
cascor-10.net ...
Conx using seed: 1156350065.57
---------##@@@@@@@@@@#32#------###############-------------------
-----------#@@(((((((@@o32#-----#((@@#########-------------------
-------------#@(((((((((@442#----#(110(@@@#######################
--------------#@(((00000((@442#---#@.332.0(@@####################
----------------#(000000000(1442#---#(2444321.0@#################
-------------#@(00oooooooooo0(4441#-###033(@o23210(@#############
@##-----#0.1111111111111111111o0+441#####---#@133332.(@@#########
(@@@##---#01222222222222222222111.++4o###-----#(244443210(@@####-
((((((@@###(13333333333333221------2+++4++3#---##o34444431@##----
0000000(((@@(2344333333321-----------4+++++++#---#@14444(#-----##
00000000000000144444321.-----------+++-4+++++++3--##02##@@@((((((
ooooooooooooooo134321------+++++++++++----++++++###--@((000000000
#############(++44-----++++++++++++++-------@++4#---#@(0000000000
@((0000o0000000000oo(1+444+++----++++---###-02..1111111111.111122
11111111111234+++4#--3+++++++--------------+++++##--2444444444444
1111111111223++444------++++-----------++++++0(@#@0..............
222222233344(144++@-------#+---+++++++++++o0(@#####01111111111111
444+++++42####034+++4-------#+++++++++++0(@@@@@@@##@(233222111111
+++++4430@#####@.44+++4@--#---(++++++0((@@@@@@@@@@@@@024443322222
++444433210(@####(24+++++444.#--o000((((((((((((((((((014+++44333
4444444444332o(@@@@034+++444440##-1.0000000000000000000o14+++++44
444444444444443210(@(.32@@1444+40###21..........11234++++++++++++
44444444444444444431o0(@###(24+++4(##0211111111124+++++++++++++++
4444444444444444444443321o(@@o34+++4(##3221111122234+++++++++++++
444444444444444444444444333210024++++4(##322222222234++++++++++++
++++++++++++++++++++44444444433224+++++4(@.332222222334++++++++++
++++++++++++++++++++444444444444444++++++4(@4333333333344++++++++
cascor-11.net ...
Conx using seed: 1156337256.9
--------#(1221111.o(@#31-----------##@@@@#####-------------------
----------#(11111.oo0(#(3o---------#@(@@@@####-------------------
------------#(.11..o00(@#32(---##@((.1.0(@@####------------------
#-------------#(o..oo00((@#32@-##@(.34443.0((###-----------------
(##-------------@0ooo000((@#(31#(@@@(24+++4442o@##---------------
##-----------#@(00o00000(((@@#32.@0@@@(2441o344420@##------------
0(#-----#(0..oo0000((((((00o.o@#32.4(@#@@#-##03444320@#----------
1.0(@#---#(o.oo000014+++++++++++++4334@####---#03444431(##-------
11..00(@#--@0..o00o24++++++++------++++++++(#---#o3444432(-------
111.oo00(@@#@0221..24+++++-----------++++++++@----#.3443#--------
111..o000(((@(03432234+4-----------+++-+++++++++----@2-##@@((((@@
2111.oo000((((0122((@------+++++++++++----++++++###--(oooo000((((
########-----#4+44-----++++++++++++++-------(+++#---#@00oo000((((
((00o..11111...ooooo@1+444+++----++++---###-03.....ooo00000oo.112
32222111..1134+++4---2+++++++--------------+++++##-#4+++++4444444
32222111....2++444------++++-----------++++++322((012222111..o000
33322223344+(3++++---------+---+++++++++++#-#@((@#@123222111.oo00
+++++++++4@##@o4++++3--------+++++++++++-----#(oo0((13433211..o00
++++++++2(@####@.4+++42--------++++++--------#(.11.oo13++43211oo0
++++++++4420@####@14+++44443#@@#-------------#01111..o.24+++4321o
+++++++++++431(@###@144+433432#o(@43.o.112222221111..oo124+++++42
+++++++++++++4431(###@.0##(233313o(@43322211111.11234+++++++++++4
++++++++++++++++443.(###---#(2333240@24322111...13+++++++++++++44
++++++++++++++++++444221o@###@o2344+3(@432211..oo.24+++++++++++++
+++++++++++++++++++44443321o0o22344+++2(@43211.oo00o24+++++++++++
++++++++++++++++++++44443333234+++++++++.@2421..o0000024+++++++++
++++++++++++++++++++44444333344+++++++++++0@432.o0000((024+++++++
cascor-12.net ...
Conx using seed: 1156360733.36
-------#(34+421.o00(#-+4#----------#@@(@@@@@@#######-------------
---------#03421.oo00(@#@+4---------#@(((@@@@########-------------
-----------#01ooo0000((@-++3--#(0#@(.210((@@#######--------------
(##----------#@@000000((@#-+41#0.1(034443100(@######-------------
o(##------------#(000((((@@#@+2#21o@@.4+++44431(@###-------------
@#----------#@o(@((((((((@@@##21(#2(##@144o034443.(###-----------
0(#-----@.2333331@@###@@@@((00@-2.(3@####---#(344442o@##---------
1.o(@#---#o2333220@(24++++++++++++4233##-#----#034444320@#-------
11.oo0(@###(233321(03++++++++------4+++++++@----#034444430-------
11..oo00((@@(13433.03+++++-----------++++++++#----#o3443#--------
11..oo0000((((1444421344-----------+++-++++++++4----@2##@((000000
11..oo00000((0o2341##------+++++++++++----++++++--#--(.111...oo00
#####--------#++++-----++++++++++++++-------#++4----#@0.....oo000
@@((00o.11111111112202+444+++----++++---###-(1((0000000000o.11223
1111..ooooo134++++#--4+++++++--------------+++++----4++++++++4444
111..ooo000o2++4++------++++-----------++++++440#@(.12211111..oo0
111111122344(3++++#--------+---+++++++++++##@0(####022221111..oo0
+++++++++4@##@.4++++4--------+++++++++++-----@1o@@#@02332211..oo0
++++++++1@#####@14++++3-------#++++++--------@120(@@@(2444321..o0
++++++++431(@####@14++++4+44@@(#------------#(231((@@@(.4+++432.o
++++++++++443.(####@24+++44443@2o(+311223333444330@@@@@(o3+++++42
++++++++++++4442o@###@1.##03442(420(443332222222232.34++++++++++4
++++++++++++++444320@###---#o33.0(4(-3433222211124++++++++++++442
++++++++++++++44444432110@###@120o140#-+4322111111334++++++++++44
+++++++++++++++4444444332210(o234124++@--+3221111...014++++++++++
++++++++++++++44444444333322234+++++++++#-343211..o0(#@14++++++++
++++++++++++++44444443333332334++++++++++4#-+4211.o0(#-#@24++++++
cascor-13.net ...
Conx using seed: 1156385936.54
oo0000o24++++42111o(#-++#-------------#--------------------------
.o000000o24++42111..0(-#+4#--##------###-------------------------
1.o0000(((02441111..oo0@-++4##021-##@(@###-----------------------
4321o00(((((0210....ooo0(#-++2@233@#2+++4(###--------------------
43210(((@@@@@(o#@0oooo0000@##+0-442##(+++++++3@#-----------------
@##-------##0230@@@(((((((((@-o(#-4(--#1++@#3++++(#--------------
(@#-----#0122222(--------###@@#-o@#2#--------#++++++1#-----------
o00(@#---#(.111.0##o4++++++++++++++4++---------@+++++++4#--------
oo000(@##-#@o111o@(24++++++++------++++++++#-----3+++++++4-------
.oo0000((@##@o2321.34+++++-----------++++++++------+++++---------
.oo00000(((@@(o4++++34++-----------+++-+++++++++----0+--##@@@@@@@
.oo00000((((((013+0##------+++++++++++----++++++-----@(00((((((@@
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