Distribution of nonces and hashes - Revision history

Geremia: /* Distribution of Nonces */ added more explanation about why the nonce distribution is skewed toward lower nonce values

2015-03-14T02:08:43Z

Distribution of Nonces: added more explanation about why the nonce distribution is skewed toward lower nonce values

← Older revision		Revision as of 02:08, 14 March 2015
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	==Histograms==		==Histograms==
	===Distribution 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:<br>[[File:Nonces Histogram.png\|histogram 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===		===Distribution of Hashes===

Geremia: /* Histograms */ added headings

2015-03-14T01:02:00Z

Histograms: added headings

← Older revision		Revision as of 01:02, 14 March 2015
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	==Histograms==		==Histograms==
			===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:<br>[[File:Nonces Histogram.png\|histogram 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:<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)]]
	<br>		<br>

Geremia: /* Histograms */ added Wikipedia:Selection bias link

2015-03-14T01:00:09Z

Histograms: added Wikipedia:Selection bias link

← Older revision		Revision as of 01:00, 14 March 2015
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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]]		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]]

	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]]

Geremia: added nonce, hash, and 2-D nonce vs. hash histograms

2015-03-14T00:57:02Z

added nonce, hash, and 2-D nonce vs. hash histograms

← Older revision		Revision as of 00:57, 14 March 2015
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	[[~~Nonce~~]] values ~~vs.~~ [[hash\|hashes]] for all the valid blocks in the [[blockchain]]:<ref>https://bitcoin.stackexchange.com/q/36414/4334</ref>		Here we analyze the [[nonce]] values and [[hash\|hashes]] for all the valid blocks in the [[blockchain]]:<ref>https://bitcoin.stackexchange.com/q/36414/4334</ref>

	====Nonces vs Hashes (y-axis logarithmic, x-axis linear)====		==Time Evolution==
			===Nonces vs Hashes (y-axis logarithmic, x-axis linear)===
	This plot readily shows that the distribution of [[nonce\|nonces]] that produce valid [[hash\|hashes]] is uniform.<br>[[File:Nonces vs Hashes.png\|verba alia]]		This plot readily shows that the distribution of [[nonce\|nonces]] that produce valid [[hash\|hashes]] is uniform.<br>[[File:Nonces vs Hashes.png\|verba alia]]

	====Nonces vs Hashes (log-log scale)====		===Nonces vs Hashes (log-log scale)===
	[[File:Nonces vs Hashes (log-log scale).png\|Nonces vs Hashes (log-log scale)]]		[[File:Nonces vs Hashes (log-log scale).png\|Nonces vs Hashes (log-log scale)]]

	In the animated version of this last plot,<ref>cf. [https://i.imgur.com/W08tgUr.gif animated version (incremental, 1k blocks shown at a time)] or [https://i.imgur.com/3LkacLD.gif animated version (cumulative)]</ref> you can really visualize the change in the [[difficulty]] and even see where the [[difficulty]] was decreased.		In the animated version of this last plot,<ref>cf. [https://i.imgur.com/W08tgUr.gif animated version (incremental, 1k blocks shown at a time)] or [https://i.imgur.com/3LkacLD.gif animated version (cumulative)]</ref> you can really visualize the change in the [[difficulty]] and even see where the [[difficulty]] was decreased.

			==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]]

			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 histogram of hashes and nonces (logarithmic color scale):<br>[[File:Density Plot (log colorscale).png\|Density Plot (log colorscale)]]
			<br>
			This also illustrates very well that the distribution of nonces is uniform.

	==References==		==References==

Geremia: Created page with "Nonce values vs. hashes for all the valid blocks in the blockchain:https://bitcoin.stackexchange.com/q/36414/4334 ====Nonces vs Hashes (y-axis log..."

2015-03-12T13:05:09Z

Created page with "Nonce values vs. hashes for all the valid blocks in the blockchain:<ref>https://bitcoin.stackexchange.com/q/36414/4334</ref> ====Nonces vs Hashes (y-axis log..."

New page

[[Nonce]] values vs. [[hash|hashes]] for all the valid blocks in the [[blockchain]]:<ref>https://bitcoin.stackexchange.com/q/36414/4334</ref>

====Nonces vs Hashes (y-axis logarithmic, x-axis linear)====
This plot readily shows that the distribution of [[nonce|nonces]] that produce valid [[hash|hashes]] is uniform.<br>[[File:Nonces vs Hashes.png|verba alia]]

====Nonces vs Hashes (log-log scale)====
[[File:Nonces vs Hashes (log-log scale).png|Nonces vs Hashes (log-log scale)]]

In the animated version of this last plot,<ref>cf. [https://i.imgur.com/W08tgUr.gif animated version (incremental, 1k blocks shown at a time)] or [https://i.imgur.com/3LkacLD.gif animated version (cumulative)]</ref> you can really visualize the change in the [[difficulty]] and even see where the [[difficulty]] was decreased.

==References==
<references />

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