Technologies: Difference between revisions
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Technologies are [[Research|researched]] in [[lab]]s using [[science pack]]s. | {{Languages}} | ||
[[File:Technology tree.png|thumb|right|280px|The technology tree − Click to enlarge.]] | |||
[[File:tech_bonuses.png|thumb|right|280px|Researched tech bonuses.]] | |||
'''Technologies''' are [[Research|researched]] in [[lab]]s using [[science pack]]s. | |||
Every technology needs certain amount of science packs | Every technology needs a certain amount of science packs per science pack type to be researched, for example the [[Logistics (research)|Logistics]] technology requires 20 [[automation science pack]]s to be placed in labs while the technology is selected for research. | ||
== Achievements == | == Achievements == | ||
{{ | {{Achievement|tech-maniac}} | ||
* 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. | |||
{{clear}} | |||
== Infinite technologies == | |||
While most technologies in Factorio are either one-off or have a finite, relatively small number of levels available, a few 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. The per-level bonuses are constant for a particular infinite technologies and, like finite research bonuses, are additive within a single technology. They are subject to diminishing returns; thus, the per-level and per-science pack contributions from very high levels of infinite technologies will eventually provide only marginal improvements. | |||
All infinite technologies levels require [[space science pack]]s, and are also the only technologies that do. As such, they are late-game technologies intended primarily for players who wish to continue playing and expand their factory past the nominal victory condition of launching a rocket. | |||
Infinite technologies are identified in-game by a small <code>∞</code> infinity symbol shown in the top right corner of the research technology's card in the research screen. | |||
Most infinite technologies are continuations of ordinary multi-level technologies; 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 technologies (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. In either case, once the first infinite level is researched, the card label switches to the one discussed above. | |||
=== | === Pricing formulas === | ||
The price of all infinite technologies is generated in a [[Wikipedia:Progression|mathematical progression]]; for the majority of technologies, the progression is [[Wikipedia:Geometric_progression|geometric]], mostly in powers of 2. Two technologies - [[mining productivity (research)|mining productivity]] and [[follower robot count (research)|follower robot count]] - use an [[Wikipedia:Arithmetic_progression|arithmetic progression]] instead. | |||
The table below summarizes for all infinite researches their first infinite level, the cost of the first few infinite levels, the cost formula and the per-level bonus. | |||
We denote by <code>N</code> the current level of the research, by <code>F</code> the final non-infinite level of the research (hence F+1 is the first "infinite" level) and by <code>P[N]</code> the price of the research at level <code>N</code>. | |||
=== | {|class="wikitable" | ||
! Technology !! Bonus !! Science Packs !! F+1 !! P[N] !! P[F+1] !! P[F+2] !! P[F+3] !! P[F+4] !! P[F+5] !! ... | |||
|- | |||
| {{Icontech|Worker robot speed (research)}} [[Worker robot speed (research)|Worker robot speed]] || +65% Robot Speed || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|6 || 1,000 × 2^(N - F - 1) || style=text-align:center|1,000 || style=text-align:center|2,000 || style=text-align:center|4,000 || style=text-align:center|8,000 || style=text-align:center|16,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Mining productivity (research)}} [[Mining productivity (research)|Mining productivity]] || +10% Mining Productivity || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|4 || 2,500 × (N - F) || style=text-align:center|2,500 || style=text-align:center|5,000 || style=text-align:center|7,500 || style=text-align:center|10,000 || style=text-align:center|12,500 || style=text-align:center|+2500 | |||
|- | |||
| {{Icontech|Physical projectile damage (research)}} [[Physical projectile damage (research)|Physical projectile damage]] || +40% Bullet Damage <br> +70% Turret Damage <br> +40% Shotgun Shell Damage <br> +100% Cannon Shell Damage || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|7 || 1,000 × 2^(N - F - 1) || style=text-align:center|1,000 || style=text-align:center|2,000 || style=text-align:center|4,000 || style=text-align:center|8,000 || style=text-align:center|16,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Stronger explosives (research)}} [[Stronger explosives (research)|Stronger explosives]] || +50% Rocket Damage <br> +20% Grenade Damage <br> +20% Landmine Damage || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|7 || 1,000 × 2^(N - F - 1) || style=text-align:center|1,000 || style=text-align:center|2,000 || style=text-align:center|4,000 || style=text-align:center|8,000 || style=text-align:center|16,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Refined flammables (research)}} [[Refined flammables (research)|Refined flammables]] || +20% Flamethrower Damage|| {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|7 || 1,000 × 2^(N - F - 1) || style=text-align:center|1,000 || style=text-align:center|2,000 || style=text-align:center|4,000 || style=text-align:center|8,000 || style=text-align:center|16,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Energy weapons damage (research)}} [[Energy weapons damage (research)|Energy weapons damage]] || +70% Laser Damage<br> +70% Electric Damage<br> +30% Beam Damage || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|7 || 1,000 × 2^(N - F - 1) || style=text-align:center|1,000 || style=text-align:center|2,000 || style=text-align:center|4,000 || style=text-align:center|8,000 || style=text-align:center|16,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Artillery shell range (research)}} [[Artillery shell range (research)|Artillery shell range]] || +30% Artillery Shell Range || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|1 || 1,000 × 2^N || style=text-align:center|2,000 || style=text-align:center|4,000 || style=text-align:center|8,000 || style=text-align:center|16,000 || style=text-align:center|32,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Artillery shell shooting speed (research)}} [[Artillery shell shooting speed (research)|Artillery shell speed]] || +100% Artillery Speed || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|1 || 1,000 + 1,000 × 3^(N - F - 1) || style=text-align:center|2,000 || style=text-align:center|4,000 || style=text-align:center|10,000 || style=text-align:center|28,000 || style=text-align:center|82,000 || style=text-align:center|×3 then - 2000 | |||
|- | |||
| {{Icontech|Follower robot count (research)}} [[Follower robot count (research)|Follower robot count]] || +25 Follower Robots || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Production science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|5 || 1000 × (N - F) || style=text-align:center|1,000 || style=text-align:center|2,000 || style=text-align:center|3,000 || style=text-align:center|4,000 || style=text-align:center|5,000 || style=text-align:center|+1000 | |||
|} | |||
==== Space Age ==== | |||
The table below summarizes all the infinite technologies in Space Age. Some are unique to Space Age, while some have their price and/or effect changed from the base game. | |||
=== [[ | {|class="wikitable" | ||
! Technology !! Bonus !! Science Packs !! F+1 !! P[N] !! P[F+1] !! ... | |||
|- | |||
| {{Icontech|Worker robot speed (research)}} [[Worker robot speed (research)|Worker robot speed ]] || +65% Robot Speed || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Electromagnetic science pack}} || style=text-align:center|7 || 1,000 × 2^(N - F) || style=text-align:center|2,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Mining productivity (research)}} [[Mining productivity (research)|Mining productivity]] || +10% Mining Productivity || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} || style=text-align:center|3 || 1,000 × (N - F) || style=text-align:center|1,000 || style=text-align:center|+1,000 | |||
|- | |||
| {{Icontech|Physical projectile damage (research)}} [[Physical projectile damage (research)|Physical projectile damage]] || +40% Bullet Damage <br> +70% Turret Damage <br> +40% Shotgun Shell Damage <br> +100% Cannon Shell Damage || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|7 || 1,000 × 2^(N - F - 1) || style=text-align:center|1,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Artillery shell range (research)}} [[Artillery shell range (research)|Artillery shell range]] || +30% Artillery Shell Range || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Metallurgic science pack}} || style=text-align:center|1 || 1,000 × 2^(N-1) || style=text-align:center|1,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Artillery shell shooting speed (research)}} [[Artillery shell shooting speed (research)|Artillery shell speed]] || +100% Artillery Speed || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Metallurgic science pack}} || style=text-align:center|1 || 1,000 × 2^(N-1) || style=text-align:center|1,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Artillery shell damage (research)}} [[Artillery shell shooting damage|Artillery shell damage]] || +10% Artillery damage || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Metallurgic science pack}} || style=text-align:center|1 || 1,000 × 2^(N-1) || style=text-align:center|1,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Stronger explosives (research)}} [[Stronger explosives (research)|Stronger explosives]] || +50% Rocket Damage <br> +20% Grenade Damage <br> +20% Landmine Damage || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Agricultural science pack}} || style=text-align:center|7 || 1,000 × 2^(N - F - 1) || style=text-align:center|1,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Laser weapons damage (research)}} [[Laser weapons damage (research)|Laser weapons damage]] || +70% Laser Damage || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|7 || 1,000 × 2^(N - F - 1) || style=text-align:center|1,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Refined flammables (research)}} [[Refined flammables (research)|Refined flammables]] || +20% Flamethrower Damage || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Agricultural science pack}} || style=text-align:center|7 || 1,000 × 2^(N - F - 1) || style=text-align:center|1,000 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Follower robot count (research)}} [[Follower robot count (research)|Follower robot count]] || +25 Follower Robots || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Military science pack}} {{icon|Production science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} || style=text-align:center|5 || 1000 × (N - F) || style=text-align:center|1,000 || style=text-align:center|+1000 | |||
|- | |||
| {{Icontech|Steel plate productivity (research)}} [[Steel plate productivity (research)|Steel plate productivity]] || +10% Steel plate recipe productivity bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} || style=text-align:center|1 || 1000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Low density structure productivity (research)}} [[Low density structure productivity (research)|Low density structure productivity]] || +10% Low density structure recipe productivity bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Metallurgic science pack}} || style=text-align:center|1 || 1000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Scrap recycling productivity (research)}} [[Scrap recycling productivity (research)|Scrap recycling productivity]] || +10% Scrap recycling recipe productivity bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Electromagnetic science pack}} || style=text-align:center|1 || 500 × 1.5^N || style=text-align:center|750 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Processing unit productivity (research)}} [[Processing unit productivity (research)|Processing unit productivity]] || +10% Processing unit recipe productivity bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Electromagnetic science pack}} || style=text-align:center|1 || 1000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Electric weapons damage (research)}} [[Electric weapons damage (research)|Electric weapons damage]] || +70% Tesla damage <br> +70% Electric damage <br> +30% Beam damage || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Military science pack}} {{icon|Chemical science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Electromagnetic science pack}} || style=text-align:center|4 || 1000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Plastic bar productivity (research)}} [[Plastic bar productivity (research)|Plastic bar productivity]] || +10% Plastic bar recipe productivity bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Agricultural science pack}} || style=text-align:center|1 || 1000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Rocket fuel productivity (research)}} [[Rocket fuel productivity (research)|Rocket fuel productivity]] || +10% Rocket fuel recipe productivity bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Agricultural science pack}} || style=text-align:center|1 || 1000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Health (research)}} [[Health (research)|Health]] || +50 Character health || {{icon|Military science pack}} {{icon|Utility science pack}} {{icon|Agricultural science pack}} || style=text-align:center|1 || 50 × 2^N || style=text-align:center|200 || style=text-align:center|×2 | |||
|- | |||
| {{Icontech|Asteroid productivity (research)}} [[Asteroid productivity (research)|Asteroid productivity]] || +10% Asteroid processing recipe productivity bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Agricultural science pack}} || style=text-align:center|1 || 1000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Railgun damage (research)}} [[Railgun damage (research)|Railgun damage]] || +40% Railgun damage bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Military science pack}} {{icon|Chemical science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Metallurgic science pack}} {{icon|Agricultural science pack}} || style=text-align:center|1 || 1000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Rocket part productivity (research)}} [[Rocket part productivity (research)|Rocket part productivity]] || +10% Rocket part recipe productivity bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Cryogenic science pack}} || style=text-align:center|1 || 2000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Railgun shooting speed (research)}} [[Railgun shooting speed (research)|Railgun shooting speed]] || +20% Railgun shooting speed bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Chemical science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Electromagnetic science pack}} {{icon|Cryogenic science pack}} || style=text-align:center|1 || 1000 × 1.5^N || style=text-align:center|1,500 || style=text-align:center|×1.5 | |||
|- | |||
| {{Icontech|Research productivity (research)}} [[Research productivity (research)|Research productivity]] || +10% Lab research productivity bonus || {{icon|Automation science pack}} {{icon|Logistic science pack}} {{icon|Military science pack}} {{icon|Chemical science pack}} {{icon|Production science pack}} {{icon|Utility science pack}} {{icon|Space science pack}} {{icon|Metallurgic science pack}} {{icon|Electromagnetic science pack}} {{icon|Agricultural science pack}} {{icon|Cryogenic science pack}} {{icon|Promethium science pack}} || style=text-align:center|1 || 1000 × 1.2^N || style=text-align:center|1,200 || style=text-align:center|×1.2 | |||
|} | |||
=== Cumulative cost === | |||
As the price of most infinite technologies (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 technologies they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful: | |||
#For infinite technologies whose underlying equation is a powers-of-two geometric series, the cumulative price of the first <code>N - F</code> infinite levels (skipping the first <code>F</code> level, so counting "infinite" levels only) 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. | |||
* | #*As ''N'' increases, this is approximated well by <code>2 × P[N] = P[N+1]</code>, so the cumulative cost of researching to level <code>N</code> is about as much as researching level <code>N+1</code>. | ||
* [ | #*If one decides a level <code>M</code> which one considers the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor of <code>X</code> will allow about <code>log[2](X)</code> 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. | ||
* [ | #*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 negates the speed benefits of their ×10 capacity expansion. | ||
#The cumulative price of the first <code>N - F</code> levels of infinite technologies whose underlying equation is an arithmetic series 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. For the [[Follower robot count (research)]], an additional <code>900 × (N-F)</code> need to be added. | |||
#*Expanding production capacity by a factor of <code>X</code>, 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). | |||
#The cumulative price of the first '''''N''''' levels of '''artillery shell shooting speed''', the sole infinite technology 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. | |||
* | |||
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.) | |||
== See also == | == See also == | ||
* [[Research]] | * [[Research]] | ||
* [[Science pack]] | * [[Science pack]] | ||
{{TechNav}} | |||
Latest revision as of 18:25, 16 November 2024
Technologies are researched in labs using science packs.
Every technology needs a certain amount of science packs per science pack type to be researched, for example the Logistics technology requires 20 automation science packs to be placed in labs while the technology is selected for research.
Achievements
Tech maniac Research all technologies. |
- 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.
Infinite technologies
While most technologies in Factorio are either one-off or have a finite, relatively small number of levels available, a few 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. The per-level bonuses are constant for a particular infinite technologies and, like finite research bonuses, are additive within a single technology. They are subject to diminishing returns; thus, the per-level and per-science pack contributions from very high levels of infinite technologies will eventually provide only marginal improvements.
All infinite technologies levels require space science packs, and are also the only technologies that do. As such, they are late-game technologies intended primarily for players who wish to continue playing and expand their factory past the nominal victory condition of launching a rocket.
Infinite technologies are identified in-game by a small ∞
infinity symbol shown in the top right corner of the research technology's card in the research screen.
Most infinite technologies are continuations of ordinary multi-level technologies; the "infinite" mechanic becomes effective once the player reaches the card initially labeled with N - ∞
in the research tree. Only the two artillery-related technologies (artillery shell range and shooting speed) are infinite-only; for these, 1 - ∞
is shown before any levels in them are researched. In either case, once the first infinite level is researched, the card label switches to the one discussed above.
Pricing formulas
The price of all infinite technologies is generated in a mathematical progression; for the majority of technologies, the progression is geometric, mostly in powers of 2. Two technologies - mining productivity and follower robot count - use an arithmetic progression instead.
The table below summarizes for all infinite researches their first infinite level, the cost of the first few infinite levels, the cost formula and the per-level bonus.
We denote by N
the current level of the research, by F
the final non-infinite level of the research (hence F+1 is the first "infinite" level) and by P[N]
the price of the research at level N
.
Technology | Bonus | Science Packs | F+1 | P[N] | P[F+1] | P[F+2] | P[F+3] | P[F+4] | P[F+5] | ... |
---|---|---|---|---|---|---|---|---|---|---|
Worker robot speed | +65% Robot Speed | 6 | 1,000 × 2^(N - F - 1) | 1,000 | 2,000 | 4,000 | 8,000 | 16,000 | ×2 | |
Mining productivity | +10% Mining Productivity | 4 | 2,500 × (N - F) | 2,500 | 5,000 | 7,500 | 10,000 | 12,500 | +2500 | |
Physical projectile damage | +40% Bullet Damage +70% Turret Damage +40% Shotgun Shell Damage +100% Cannon Shell Damage |
7 | 1,000 × 2^(N - F - 1) | 1,000 | 2,000 | 4,000 | 8,000 | 16,000 | ×2 | |
Stronger explosives | +50% Rocket Damage +20% Grenade Damage +20% Landmine Damage |
7 | 1,000 × 2^(N - F - 1) | 1,000 | 2,000 | 4,000 | 8,000 | 16,000 | ×2 | |
Refined flammables | +20% Flamethrower Damage | 7 | 1,000 × 2^(N - F - 1) | 1,000 | 2,000 | 4,000 | 8,000 | 16,000 | ×2 | |
Energy weapons damage | +70% Laser Damage +70% Electric Damage +30% Beam Damage |
7 | 1,000 × 2^(N - F - 1) | 1,000 | 2,000 | 4,000 | 8,000 | 16,000 | ×2 | |
Artillery shell range | +30% Artillery Shell Range | 1 | 1,000 × 2^N | 2,000 | 4,000 | 8,000 | 16,000 | 32,000 | ×2 | |
Artillery shell speed | +100% Artillery Speed | 1 | 1,000 + 1,000 × 3^(N - F - 1) | 2,000 | 4,000 | 10,000 | 28,000 | 82,000 | ×3 then - 2000 | |
Follower robot count | +25 Follower Robots | 5 | 1000 × (N - F) | 1,000 | 2,000 | 3,000 | 4,000 | 5,000 | +1000 |
Space Age
The table below summarizes all the infinite technologies in Space Age. Some are unique to Space Age, while some have their price and/or effect changed from the base game.
Technology | Bonus | Science Packs | F+1 | P[N] | P[F+1] | ... |
---|---|---|---|---|---|---|
Worker robot speed | +65% Robot Speed | 7 | 1,000 × 2^(N - F) | 2,000 | ×2 | |
Mining productivity | +10% Mining Productivity | 3 | 1,000 × (N - F) | 1,000 | +1,000 | |
Physical projectile damage | +40% Bullet Damage +70% Turret Damage +40% Shotgun Shell Damage +100% Cannon Shell Damage |
7 | 1,000 × 2^(N - F - 1) | 1,000 | ×2 | |
Artillery shell range | +30% Artillery Shell Range | 1 | 1,000 × 2^(N-1) | 1,000 | ×2 | |
Artillery shell speed | +100% Artillery Speed | 1 | 1,000 × 2^(N-1) | 1,000 | ×2 | |
Artillery shell damage | +10% Artillery damage | 1 | 1,000 × 2^(N-1) | 1,000 | ×2 | |
Stronger explosives | +50% Rocket Damage +20% Grenade Damage +20% Landmine Damage |
7 | 1,000 × 2^(N - F - 1) | 1,000 | ×2 | |
Laser weapons damage | +70% Laser Damage | 7 | 1,000 × 2^(N - F - 1) | 1,000 | ×2 | |
Refined flammables | +20% Flamethrower Damage | 7 | 1,000 × 2^(N - F - 1) | 1,000 | ×2 | |
Follower robot count | +25 Follower Robots | 5 | 1000 × (N - F) | 1,000 | +1000 | |
Steel plate productivity | +10% Steel plate recipe productivity bonus | 1 | 1000 × 1.5^N | 1,500 | ×1.5 | |
Low density structure productivity | +10% Low density structure recipe productivity bonus | 1 | 1000 × 1.5^N | 1,500 | ×1.5 | |
Scrap recycling productivity | +10% Scrap recycling recipe productivity bonus | 1 | 500 × 1.5^N | 750 | ×1.5 | |
Processing unit productivity | +10% Processing unit recipe productivity bonus | 1 | 1000 × 1.5^N | 1,500 | ×1.5 | |
Electric weapons damage | +70% Tesla damage +70% Electric damage +30% Beam damage |
4 | 1000 × 1.5^N | 1,500 | ×1.5 | |
Plastic bar productivity | +10% Plastic bar recipe productivity bonus | 1 | 1000 × 1.5^N | 1,500 | ×1.5 | |
Rocket fuel productivity | +10% Rocket fuel recipe productivity bonus | 1 | 1000 × 1.5^N | 1,500 | ×1.5 | |
Health | +50 Character health | 1 | 50 × 2^N | 200 | ×2 | |
Asteroid productivity | +10% Asteroid processing recipe productivity bonus | 1 | 1000 × 1.5^N | 1,500 | ×1.5 | |
Railgun damage | +40% Railgun damage bonus | 1 | 1000 × 1.5^N | 1,500 | ×1.5 | |
Rocket part productivity | +10% Rocket part recipe productivity bonus | 1 | 2000 × 1.5^N | 1,500 | ×1.5 | |
Railgun shooting speed | +20% Railgun shooting speed bonus | 1 | 1000 × 1.5^N | 1,500 | ×1.5 | |
Research productivity | +10% Lab research productivity bonus | 1 | 1000 × 1.2^N | 1,200 | ×1.2 |
Cumulative cost
As the price of most infinite technologies (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 technologies they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:
- For infinite technologies whose underlying equation is a powers-of-two geometric series, the cumulative price of the first
N - F
infinite levels (skipping the firstF
level, so counting "infinite" levels only) is2 × P[N] - P[F+1]
; i.e., twice the price of the final researched level, less the price of the first "infinite" level.- As N increases, this is approximated well by
2 × P[N] = P[N+1]
, so the cumulative cost of researching to levelN
is about as much as researching levelN+1
. - If one decides a level
M
which one considers the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor ofX
will allow aboutlog[2](X)
additional levels to be researched before the next level takes longer to research with the expanded capacity than levelM + 1
would have taken with the pre-expansion production capacity. - For example, if one expands production capacity by a factor of 10, they will be able to research at least
floor(log[2](10)) = 3
and at mostceiling(log[2](10)) = 4
additional levels in a given technology before the exponential increase in price negates the speed benefits of their ×10 capacity expansion.
- As N increases, this is approximated well by
- The cumulative price of the first
N - F
levels of infinite technologies whose underlying equation is an arithmetic series is(N - F) × (P[N] + P[F + 1]) ÷ 2
; i.e,N - F
times the mean of the prices of the first and last "infinite" level. For the Follower robot count (research), an additional900 × (N-F)
need to be added.- Expanding production capacity by a factor of
X
, as above, will in this case allow an additionalN × (X - 1)
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).
- Expanding production capacity by a factor of
- The cumulative price of the first N levels of artillery shell shooting speed, the sole infinite technology whose underlying equation is a powers-of-three geometric series (equation type (2)) is
1.5 × P[N] - 0.5 × P[1]
; i.e., 1.5 times the price of the final researched level, less half the price of the first level.
Note that these prices reflect research units, which will not be equal to science packs if productivity modules are used in labs. (In that case, the science pack requirement will be lower.)