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| Note that inserters can take science packs from labs and hand them to other labs, making a lab chain a feasible solution. Other options include using 3 belts (before space science packs are needed), or a [[Glossary#S|sushi belt]]. | | Note that inserters can take science packs from labs and hand them to other labs, making a lab chain a feasible solution. Other options include using 3 belts (before space science packs are needed), or a [[Glossary#S|sushi belt]]. |
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| == 'Infinite' research ==
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| While most research topics in Factorio are either one-off or have a finite, relatively small number of levels available, several (14 in total) are "infinite", meaning the player can research as many levels as they can afford. All of them unlock bonuses to existing technologies, never new structures or abilities. With the exception of [[mining productivity (research)|mining productivity]] and [[worker robot speed (research)|worker robot speed]], all infinite research topics are combat-related. The per-level bonuses are constant for a particular infinite research topic and, like normal research bonuses, are additive (rather than multiplicative) within a single topic.
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| All infinite research levels require [[space science pack|space science packs]], and are also the only research topics that do. As such, they are late-game research topics intended primarily for players who wish to continue playing and expand their factory past the nominal victory condition of launching a single rocket.
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| Infinite research topics are identified in-game by a small <code>∞</code> infinity symbol shown in the top right corner of the research topic's card in the research screen. Note that this category of research topics has no official name or other distinction apart from the above; "infinite research" is a placeholder name bestowed by the community.
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| Most infinite research topics are continuations of ordinary multi-level topics; the "infinite" mechanic becomes effective once the player reaches the card initially labeled with <code>N - ∞</code> in the research tree. Only the two [[artillery]]-related topics (artillery shell [[artillery shell range (research)|range]] and [[artillery shell shooting speed (research)|shooting speed]]) are infinite-only; for these, <code>1 - ∞</code> is shown before any levels in them are researched.
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| In either case, once the first infinite level is researched, the card label switches to the one discussed above. Unlike normal leveled research, infinite research topics do not switch to a new card for every level, instead only incrementing the level number on the same card. This is likely so as to prevent the "tree" visualization of available research from becoming overly long.
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| === Pricing equations ===
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| The price of all infinite research topics is generated in a [https://en.wikipedia.org/wiki/Progression mathematical progression]; for the majority of topics, the progression is [https://en.wikipedia.org/wiki/Geometric_progression geometric], mostly in powers of 2; a single topic - [[artillery shell shooting speed (research)|artillery shell shooting speed]] - uses a powers-of-3 progression. Two topics - [[mining productivity (research)|mining productivity]] and [[follower robot count (research)|follower robot count]] - use an [https://en.wikipedia.org/wiki/Arithmetic_progression arithmetic progression] instead, in both cases with a difference of 100.
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| The equations that generate infinite research prices take the following forms:
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| #<code>P[N] = P[0] × 2 ^ (N - N[0]) + C</code> - most infinite topics
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| #<code>P[N] = P[0] × 3 ^ (N - N[0]) + C</code> - '''artillery shell shooting speed'''
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| <!-- ** specifically, the coefficients are P = 1,000; N[0] = 0; C = -1,000 -->
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| #<code>P[N] = P[0] × (N - N[0]) + C</code> - '''mining productivity''' and '''follower robot count'''
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| where:
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| *'''''P[N]''''' is the price of the '''''N'''''th level of the research topic (as reported by the game; i.e., counting also all starting "non-infinite" levels, if any)
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| *'''''P[0]''''' is a price multiplier
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| *'''''N''''' is the level of the research topic, as reported by the game (i.e., including any starting non-infinite levels)
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| *'''''N[0]''''' is a shift factor relative to the source series
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| *'''''C''''' is a constant
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| Among others, the following properties can be observed:
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| *<code>P[0] = 1,000</code> for topics with a geometric progression and <code>P[0] = 100</code> for topics with an arithmetic progression
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| *for both infinite-only topics, <code>P[1] = 2 × P[0]</code>
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| *denote <code>F</code> the final level of non-infinite research available in the topic if such exists; for infinite-only research, set <code>F = 0</code>; then:
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| *the majority of geometric-progression topics have <code>P[F+1] = P[0]</code>; the rest have <code>P[F+1] = 2 × P[0]</code> (where ''P[F+1]'' is the price of the first "infinite" level)
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| *for topics with preceding non-infinite levels, the relation between ''P[F+1]'' and non-infinite level prices may vary, but in all cases <code>P[F+1] >= P[F]</code> (where ''P[F]'' is the price of the last non-infinite level)
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| *either <code>N[0] = F</code> or <code>N[0] = F + 1</code>; this is mostly idiosyncratic to the research topic in question
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| *<code>C != 0</code> only for '''follower robot count''' (''C'' = 900) and '''artillery shooting speed''' (''C'' = 1,000)
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| === Price table ===
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| The table below summarizes the applicable equation type and parameters (using the same notation as in the preceding section), plus the per-level bonus, for all infinite research topics in the game. Topics are ordered based on similarity of the parameters; if parameters are identical, then alphabetically.
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| {| class="wikitable"
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| ! Technology !! Equation <br/> type !! F + 1 !! P[F + 1] !! Equation !! Bonus
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| | {{Icontech|Gun turret damage (research)}} [[Gun turret damage (research)|Gun turret damage]] || 1 || 7 || 1,000 || 1,000 × 2^(N - F - 1) || +70%
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| | {{Icontech|Rocket damage (research)}} [[Rocket damage (research)|Rocket damage]] || 1 || 7 || 1,000 || 1,000 × 2^(N - F - 1) || +50%
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| | {{Icontech|Bullet damage (research)}} [[Bullet damage (research)|Bullet damage]] || 1 || 7 || 1,000 || 1,000 × 2^(N - F - 1) || +40%
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| | {{Icontech|Shotgun shell damage (research)}} [[Shotgun shell damage (research)|Shotgun shell damage]] || 1 || 7 || 1,000 || 1,000 × 2^(N - F - 1) || +40%
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| | {{Icontech|Flamethrower damage (research)}} [[Flamethrower damage (research)|Flamethrower damage]] || 1 || 7 || 1,000 || 1,000 × 2^(N - F - 1) || +20%
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| | {{Icontech|Worker robot speed (research)}} [[Worker robot speed (research)|Worker robot speed ]] || 1 || 6 || 1,000 || 1,000 × 2^(N - F - 1) || +65%
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| | {{Icontech|Combat robot damage (research)}} [[Combat robot damage (research)|Combat robot damage ]] || 1 || 6 || 1,000 || 1,000 × 2^(N - F - 1) || +30%
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| | {{Icontech|Cannon shell damage (research)}} [[Cannon shell damage (research)|Cannon shell damage]] || 1 || 6 || 1,000 || 1,000 × 2^(N - F - 1) || +30%
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| | {{Icontech|Laser turret damage (research)}} [[Laser turret damage (research)|Laser turret damage]] || 1 || 8 || 1,000 || 1,000 × 2^(N - F - 1) || +70%
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| | {{Icontech|Artillery shell range (research)}} [[Artillery shell range (research)|Artillery shell range]] || 1 || 1 || 2,000 || 1,000 × 2^(N - F) || +30%
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| | {{Icontech|Grenade damage (research)}} [[Grenade damage (research)|Grenade damage]] || 1 || 7 || 2,000 || 1,000 × 2^(N - F) || +20%
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| | {{Icontech|Mining productivity (research)}} [[Mining productivity (research)|Mining productivity]] || 3 || 16 || 1,500 || 100 × (N - 1) || +2%
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| | {{Icontech|Follower robot count (research)}} [[Follower robot count (research)|Follower robot count]] || 3 || 7 || 1,000 || 100 × N + 900 || +10
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| | {{Icontech|Artillery shell shooting speed (research)}} [[Artillery shell shooting speed (research)|Artillery shell shooting speed]] || 2 || 1 || 2,000 || 1,000 × 3^(N - F - 1) + 1,000 || +100%
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| |}
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| === Affordability ===
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| Infinite research is essentially an inexhaustible resource sink for players who build very large bases. While the bonuses it provides can significantly improve the player's capabilities (particularly as regards combat), they are subject to diminishing returns; thus, the per-level contributions from very high levels of infinite research will eventually provide only marginal improvements.
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| As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:
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| #The cumulative price of the first <code>N - F</code> levels (notation as in previous sections; i.e., here counting "infinite" levels only) of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is <code>2 × P[N] - P[F+1]</code>; i.e., twice the price of the final researched level, less the price of the first "infinite" level.
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| #*This tends toward <code>2 × P[N]</code> as ''N'' goes to infinity.
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| #*The above also shows that, assuming constant research speed (usually, this is the same as science pack production capacity), each subsequent level of an infinite research topic of this type will take about as long as ''all'' preceding infinite levels took combined (or, twice as long as the previous level).
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| #*Further, assuming one has reached a level <code>M</code> they consider the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor of '''''X''''' will allow at least <code>floor(log[2](X))</code> and at most <code>ceiling(log[2](X))</code> (i.e., the next lower / higher integer from the base-2 logarithm of ''X'') additional levels to be researched before the next level takes longer to research with the expanded capacity than level <code>M + 1</code> would have taken with the pre-expansion production capacity.
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| #*For example, if one expands production capacity by a factor of 10, they will be able to research at least <code>floor(log[2](10)) = 3</code> and at most <code>ceiling(log[2](10)) = 4</code> additional levels in a given technology before the exponential increase in price wipes out the benefits of their ×10 capacity expansion.
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| #The cumulative price of the first <code>N - F</code> levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is <code>(N - F) × (P[N] + P[F + 1]) ÷ 2</code>; i.e, <code>N - F</code> times the mean of the prices of the first and last "infinite" level.
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| #*Expanding production capacity by a factor of ''X'', as above, will in this case allow an additional <code>N × (X - 1)</code> levels to be researched before the benefit of the expansion is wiped out (i.e., research progress speed drops to or below what it was pre-expansion).
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| #The cumulative price of the first '''''N''''' levels of '''artillery shell shooting speed''', the sole infinite research topic whose underlying equation is a powers-of-three geometric series (equation type (2)) is <code>1.5 × P[N] - 0.5 × P[1]</code>; i.e., 1.5 times the price of the final researched level, less half the price of the first level.
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| #*''Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.''
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| ; :In all calculations above, the constant <code>C</code> (see equations) is ignored; for the topics where <code>C ≠ 0</code>, results must be adjusted by adding <code>C × (N - F)</code>. This only applies to '''follower robot count''' and '''artillery shooting speed'''.
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| In all cases, the player can calculate the research price of their target level using the general equations (1), (2), (3) (see preceding sections), look up the price of the first "infinite" level in the table above, then use the summation properties described herein to arrive at a total science pack budget.
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| Note that these prices reflect '''research units''', which will not be equal to science packs if [[productivity module|productivity modules]] are used in labs. (In that case, the science pack requirement will be lower.)
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| == Achievements == | | == Achievements == |
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| Research is directly connected to the following achievements:
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| {{Achievement|Tech-maniac}} | | {{Achievement|Tech-maniac}} |
| *Completing "infinite" research topics of any level is not required for '''Tech maniac'''. All "non-infinite" levels of topics that have "infinite" continuations are still required. | | * Completing infinite technologies of any level is not required for '''Tech maniac'''. All non-infinite levels of technologies that have infinite continuations are still required. |
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| == History == | | == History == |
