Distribution of nonces and hashes: Difference between revisions
added nonce, hash, and 2-D nonce vs. hash histograms |
→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 selection effect: most everyone starts searching for nonces starting at 0:<br>[[File:Nonces Histogram.png|histogram of nonces]] | ===Distribution of Nonces=== | ||
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]] | |||
===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]] | ||
===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.
Nonces vs Hashes (log-log scale)
.png)
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:
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):
2-D Distribution of Nonces & Hashes
2-D histogram of hashes and nonces (logarithmic color scale):.png)
This also illustrates very well that the distribution of nonces is uniform.
References
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