Difference between revisions of "Distribution of nonces and hashes"

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m (Histograms: added Wikipedia:Selection bias link)
(Distribution of Nonces: added more explanation about why the nonce distribution is skewed toward lower nonce values)
 
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==Histograms==
 
==Histograms==
The nonces found are skewed toward 0 because this is a [[Wikipedia:Selection_bias|selection effect]]: most everyone starts searching for nonces starting at 0:<br>[[File:Nonces Histogram.png|histogram of nonces]]
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===Distribution of Nonces===
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The nonces found are skewed toward 0 because this is a [[Wikipedia:Selection_bias|selection effect]]: most everyone starts searching for nonces starting at 0, so the lower nonces are found first, even though there may be also higher nonces that could produce a winning block:<br>[[File:Nonces Histogram.png|histogram of nonces]]
  
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===Distribution of Hashes===
 
Although the distribution of hashes is not uniform, this does not matter; all that matters is that the distribution of nonces is uniform (which they are, minus the selection effect of starting at 0):<br>[[File:Hashes Histogram.png|histogram of hashes]]
 
Although the distribution of hashes is not uniform, this does not matter; all that matters is that the distribution of nonces is uniform (which they are, minus the selection effect of starting at 0):<br>[[File:Hashes Histogram.png|histogram of hashes]]
  
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===2-D Distribution of Nonces & Hashes===
 
2-D histogram of hashes and nonces (logarithmic color scale):<br>[[File:Density Plot (log colorscale).png|Density Plot (log colorscale)]]
 
2-D histogram of hashes and nonces (logarithmic color scale):<br>[[File:Density Plot (log colorscale).png|Density Plot (log colorscale)]]
 
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Latest revision as of 02:08, 14 March 2015

Here we analyze the nonce values and hashes for all the valid blocks in the blockchain:[1]

Time Evolution

Nonces vs Hashes (y-axis logarithmic, x-axis linear)

This plot readily shows that the distribution of nonces that produce valid hashes is uniform.
verba alia

Nonces vs Hashes (log-log scale)

Nonces vs Hashes (log-log scale)

In the animated version of this last plot,[2] you can really visualize the change in the difficulty and even see where the difficulty was decreased.

Histograms

Distribution of Nonces

The nonces found are skewed toward 0 because this is a selection effect: most everyone starts searching for nonces starting at 0, so the lower nonces are found first, even though there may be also higher nonces that could produce a winning block:
histogram of nonces

Distribution of Hashes

Although the distribution of hashes is not uniform, this does not matter; all that matters is that the distribution of nonces is uniform (which they are, minus the selection effect of starting at 0):
histogram of hashes

2-D Distribution of Nonces & Hashes

2-D histogram of hashes and nonces (logarithmic color scale):
Density Plot (log colorscale)
This also illustrates very well that the distribution of nonces is uniform.

References

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