Tuesday, July 16, 2024

Physics - Dynamics

Dynamics


Introduction

Newton's Second Law

$$\begin{equation} \mathbf{F} = m\mathbf{a}= m \frac{d\mathbf{v}}{dt} = \frac{d^2\mathbf{x}}{dt^2} \end{equation}$$

Newton's Third Law

The force exerted by object $i$ onto object $j$ is opposite of the force exerted by object $j$ onto object $i$. (We use lower case $f$ for internal forces):

$$\begin{equation} \mathbf{f}_{ij} = - \mathbf{f}_{ji} \end{equation}$$

External Force

Denote the total external force exerted on object $i$ as (we use upper case $F$ for external forces) $\mathbf{F}_i$.


Applications

One object without external force

$\mathbf{F} = 0$, therefore, $\frac{d\mathbf{v}}{dt} = 0$, i.e., $\mathbf{v}$ does not change. The trajectory of the object is:

$\mathbf{x} = \mathbf{x}_{0} + \mathbf{v}t$.

One object with constant force (same direction)

$\mathbf{a} = \frac{\mathbf{F}}{m}$

$\mathbf{x} = \mathbf{x}_0 + \mathbf{v}_0t + \frac{1}{2}\mathbf{a}t^2$

Average velocity:

$\bar{\mathbf{v}} = \frac{1}{2}(\mathbf{v}_0 + \mathbf{v}_f)$

Time spent:

$t = \frac{\mathbf{v}_f - \mathbf{v}_0}{\mathbf{a}}$

Total distance:

$\mathbf{S} = \bar{\mathbf{v}}t= \frac{1}{2}(\mathbf{v}^2_f - \mathbf{v}^2_0)$

Two objects without external force

$$\mathbf{f}_{ji} = m_i \frac{d\mathbf{v}_i}{dt}$$

$$\mathbf{f}_{ij} = m_j \frac{d\mathbf{v}_j}{dt}$$

The sum gives (uses Equation (2)):

$$\begin{equation} m_i \frac{d\mathbf{v}_i}{dt} + m_j \frac{d\mathbf{v}_j}{dt} = 0 \end{equation}$$

Rewritten as:

$$\frac{d (m_i \mathbf{v}_i + m_j \mathbf{v}_j)}{dt} = 0$$

Conservation of momentum:

$$\begin{equation} m_i \mathbf{v}_i + m_j \mathbf{v}_j = const \end{equation}$$

Equation (3) can also be written as:

$$\begin{equation} m_i \frac{d^2\mathbf{x}_i}{dt^2} + m_j \frac{d^2\mathbf{x}_j}{dt^2} =
\frac{d^2 (m_i \mathbf{x}_i + m_j \mathbf{x}_j)}{dt^2} = 0 \end{equation}$$

If we define the center of mass as:

$$\begin{equation} \mathbf{x}_{c} = \frac{m_{i}}{m_{i}+m_{j}}\mathbf{x}_i + \frac{m_{j}}{m_{i}+m_{j}}\mathbf{x}_j \end{equation}$$

Equation (5) becomes:

$$\begin{equation} (m_i+m_j) \frac{d^2 (\frac{m_i}{m_i+m_j}\mathbf{x}_i + \frac{m_j}{m_i+m_j} \mathbf{x}_j)}{dt^2} = (m_i+m_j) \frac{d^2 (m_i+m_j)\mathbf{x}_c}{dt^2} = 0 \end{equation}$$

Therefore, we can view the two objects as one object with mass $m_i+m_j$ and their center of mass $\mathbf{x}_c$ moves with a constant velocity.

If there are external forces, we can repeat the process, the result is as if the total external forces act on the center of mass of the whole system.


Saturday, February 8, 2020

轮回

今天在Coronavirus肆虐武汉之际,读完了毕淑敏的《花冠病毒》。其中的一段关于轮回的描写和我的宗教观非常吻合。抄录于此,也以此纪念去年因癌症去世的一位朋友。

294-297页

人是元素,这个大前提前世就定了下来,后天或许能改变一些轻微的组分,但不能改变根本的性质。

当罗纬芝知道了那个拯救了自己的白娘子,学名是“锗”以后,就开始对元素产生了浓厚的兴趣。前一段时间检索了大量资料。她原本聪颖,加之李元的循循善诱,奇妙的科学信息汇拢在一起,犹如世间神话,让她如痴如醉。

阳光透过没有关闭好的窗帘,映射到罗纬芝的身上,这让她残旧白绸一样光滑而暗淡的脸庞,泛出似有似无的红色。她感到微微的热。啊,连这号称太阳的伟大天体,也不过主要是由氢和氦构成的炙热火团,当然,它不会单纯到只有这两种元素,还有氧,碳,硅,铁,硫等成分。它亿万年地向四周喷射着光焰和热力,从来没有要求过任何感谢,人和它相比是何等的功利和琐碎啊。恒星的运转,主要靠氢的燃烧。似乎无穷无尽的氢,也终有燃烧耗尽之时。那时候星体就无可挽救地开始熄火,逐渐停止运转。在这个悲惨而壮丽地过程中,星体会发生很矛盾的两极变化。它的内部持续收缩,而星体外侧的物质,则放任不羁地开始扩张。没落的恒星像气球一样膨胀,进入到红巨星状态,星体内核这一收缩不要紧,马上造成星体内温度的急剧上升,居然可以从1000万摄氏度嗖嗖的窜到1亿摄氏度。如此不可想象的高温,就引起星体内部的氦元素燃烧,聚变产生铍,铍再产生碳,再生成氧... 在内部翻天覆地倒海翻江的同时,外部也没闲着,继续锲而不舍地膨胀,直到达到可怕的极限。这是会发生什么事儿呢?恒星的外层物质众叛亲离,向宇宙深处漂流而去。而内在的聚变生成了铁。

上述过程并不是一次到位,而是不厌其烦地反复进行,且越来越快,疯狂循环。

哈!这星球老来得子的铁,是星体生命完结的最后一杯猩红的葡萄酒。星体终于迎来了自身辉煌绚烂的死亡之光。猛烈的爆发把各种元素礼花般抛向太空,遇冷凝结,这就形成了行星。原来我们赖以生存的地球就是这么诞生的,而作为地球的无心插柳的附属物---人类,那更是下游末端的产品,本不在计划之内。地球原本是枯寂世界,经过长期演变,出现了水,出现了蛋白质,出现了五彩缤纷的生命。它们从植物到动物,再到人类。种种元素的流浪和拼盘盛宴,千变万化镶嵌搭配,最终构成了精细的人体。每个人都是巨大宇宙空间的宁馨产儿,是星云的小小尾货单品,都是一堆元素的组合。所以每一个人,也就说是缩小版的地球,超微结构的宇宙。

星云中的元素构成了地球,然后转移到植物,然后再次转移到动物,之后才是人类。人类死亡,自身的元素又还给地球,多么完美的循环啊。元素是自然界的精灵。在永恒的宇宙和稍纵即逝的自然界之间,循环往复,既是信使,又是终极。

把这一切都想通之后,罗纬芝心如止水柔和淡定了。她不怕死了,她知道自己永不会完结。那些构成她血液成分的元素,现在已经借着郝辙之手,周游世界去了。那不是她的本意,却也无法控制。即使他在为苏雅输血的过程中,终结了自我生命,但它的元素依然会在苏雅体内开始新的旅途。在遥远的将来,这些曾经属于它的元素,都会和他的灵魂异地会合。在更遥远的将来,也许又如七巧板一样拼凑起来,变成一个新的罗纬芝,穿行于世。那么反过来推测,今世的罗纬芝一定也曾以元素的形式,在太空傲游。在某一个特定的框架中,父精母血(本质也是元素啦!)凝聚成了今日之人形。当然还有无数的谷物豆类精肉鸡蛋(本质也是元素啦!)填充其中,这才有了今日之她。

罗纬芝不相信罗轮回,不相信任何宗教,但她笃信元素的周而复始生生不息。相信所有的开端都必有结尾,所有的结尾又是写下新一轮诗篇的破题。相信无法逃脱大智若愚的宇宙的安排,相信洪荒寂静大风飞扬,惟有元素长存。美国的物理学家理查德*费曼说过:“如果把科学史压缩成一句话,它会是:一切东西都是由原子构成的。”

是的,罗纬芝是原子构成的,李元也是原子构成的。所有的人和物,包括奄奄一息的苏雅和横行猖獗的病毒,都是元素构成的。

既然我们的基本组成都是一样的,那我们还有什么可以惧怕和畏缩的呢?原子是不灭的。科学家们已然确知原子长寿到了不可思议的地步。到底有多长寿呢?大约为10的35万次方年!这是一个不可想象的数字,科学家为了一劳永逸,干脆偷懒,简言之“物质不灭”。在这个无比漫长的空间里,不安分的原子到底是怎么度过的呢?它们无拘无束,四处漫游。罗纬芝自信自己身上的某个原子,已经轻车熟路地穿越过若干恒星和卫星,曾化身过百万种生物的组成部分,然后才屈尊成为了自己的肉身。

当自己的这百十斤溃灭之后,那些原子(当然也包括病毒的原子)就会袅袅飘然而去,开始了新的一轮轮回。如果说是废物利用,就有点狂妄,把自己这一次的过程夸大了,更准确的说是改头换面柳暗花明又一村。原子飘呀飘的,也许会成为伟人或是凡人的组成部分,不过这个概率应该是很低的,最大的可能是一头栽进了大海。因为海洋占据了地球上70%的份额,所以我们每个人成为海水的可能性也就占了三分之二。剩下的那三分之一的可能性,喜欢轻盈的,你可以变作风;喜欢沉重的,你可以化作铅;喜欢洁净的,你可以凝成一滴露珠;喜欢美味的,你可以变成红烧肉... 凡此种种,皆有可能。

有好事的科学家计算过,每个人身上多达10亿个原子,就像10亿个螺丝钉,不过通通是生命的配件。记住他们还是标准配件,很多人都使用过的。比如这些螺丝钉可能分别来自北京猿人,屈原,释迦摩尼,贝多芬或是强盗娼妓杀人犯... 他们的原子在世界游荡,被你所俘获,再次组配。我们可能都是别人转世化身而来,而且时时刻刻准备着再次摇身一变,幻化为万象。虽然人的这一世非常短暂,但构成我们身体的这些物质,具体说来就是原子,千秋万代永恒存在。甚至比地球更加古老,因为地球的生成才几十亿年,早在宇宙大爆炸之前,我们就已经优哉游哉地荡漾了。这不是宗教,不是迷信,而是科学。物质不灭,能量守恒。化学中的分子量平衡,说穿了不就是这么回事吗?就连爱因斯坦的能量公式,其本质也是平衡和不灭。

这就是科学界的原子轮回观。困惑是通往清晰的必由之路。明白了这一点,罗纬芝勇气倍增。每个人都要有自己灵魂的解药。多少年来害怕死亡,经受恐惧死亡的煎熬,曾是罗纬芝生命中最大的黑洞。现在他已被精确的填满,从此平复如荒漠之沙。这并不导向虚无,而是高贵的人性在顿悟中蒸馏而出。元素的循环往复以至无穷,让世间之人放下斤斤计较自私利己的心魔。当罗纬芝距离死亡最近的时刻,她嫣然一笑,不再害怕死亡了。这一个变化,让她欣喜莫名,安然的享受到了生命纯粹的快乐。原来这万物的真实性,就是不生,不灭,无来也无去,好像光的无数次轮回,永不熄灭。

Saturday, March 25, 2017

Beyond Gen II

This is my own note for how to prepare for future generations, based on two references: one and two.

Generation III (nothing to prepare for)

Babies (requires hatching):
Azurill (Marill baby)
Wynaut (Wobbuffet baby)
Non-babies (can be caught in wild):
Ralts> Kirlia > Gardevor (25, and 100 candies)
Nosepass
Roselia
Duskull > Dusclops (50 candies)
Chimecho
Snorunt > Glalie (50 candies)
Clamperl > Gorebyss (50 candies, evo item: deepseascale)
Clamperl > Huntail (50 candies, evo item: deepseatooth)
Feebas > Milotic (50 candies, evo item: prism scale, item introduced in Gen5?)

Generation IV (Need to save candies)

Babies (require hatching):
Happny (Chansey baby)
Mime Jr. (Mr. Mime baby)
Munchlax (Snorlax baby)
Bonsly (Sudowoodo baby)
Mantyke (Mantine baby)
Chingling (Chimecho (gen 3) baby) 
Evolutions from previous generation:
Magneton > Magnezone (100 candies, no evo item)
Lickitung > Likilicky (50 candies, evo item: rollout)
Rhydon > Rhyperior (100 candies, evo item: protector)
Tangela > Tangrowth (50 candies, evo item: ancient power)
Electabuzz > Electivire (50 candies, evo item: electrizer)
Magmar > Magmortar (50 candies, evo item: magmarizer)
Eevee > Leafeon (25 candies, evo item: moss rock)
Eevee > Glaceon (25 candies, evo item: ice rock)
Porygon2 > Porygon-Z (most likely 50 candies from Porygon instead of Porygon2 based on the past pattern, evo item: dubious disc)
Togetic > Togekiss (most likely 50 candies from Togepi instead of Togetic based on past pattern, evo item: shiny stone)
Aipom > Ambipom (50 candies, evo item: double hit)
Yanma > Yanmega (50 candies, evo item: ancient power)
Murkrow > honchkrow (50 candies, evo item: dusk stone)
Misdreavus > Mismaguis (50 candies, evo item: dusk stone)
Gilgar > Gliscor (50 candies, evo item: razor fang)
Sneasel > Weavile (50 candies, evo item: razor claw)
Piloswine > Mamoswine (most likely 100 candies from Swinub based on past pattern, evo item: ancient power)
Kirlia (Gen3) > Gallade (100 candies, evo item: dawn stone)
Nosepass (Gen3) > Probopass (50 candies)
Roselia (Gen3) > Roserade (100 candies, evo item: shiny stone)
Dusclops (Gen3) > Dusknoir (100 candies, evo item: reaper cloth)
Snorunt (Gen3) > Froslass (50 candies, evo item: dawn stone)

Generation V
Non-babies (can be caught in wild):
Cottonee > Whimsicott (50 candies, evo item: sun stone)
Lampent > Chandelure (50 candies, evo item: dusk stone)
Petilil > Lilligant (50 candies, evo item: sun stone)

Generation VI

Non-babies (can be caught in wild):
Helioptile > Heliolisk (50 candies, evo item: sun stone)
Doublade > Aegislash (50 candies, evo item: dusk stone)
Spritzee > Aromatisse (50 candies, evo item: sachet)
Swirlix > Slurpuff (50 candies, evo item: whipped dream)

Evolutions from previous generation:
Eevee > Sylveon (25 candies, evo item: affection, fair-type move?)

Generation VII

Evolutions from previous generation:
Pikachu > Raichu* (50 candies, a different Raichu, evo item: thunder stone)
Exeggcute > Exeggutor* (50 candies, a different Exeggutor, evo item: leaf stone)
Cubone > Marowak* (50 candies, a different Marowak, at night, no evo item)

Friday, March 10, 2017

The Secret of Egg Hatching

The mystery behind egg-hatching has been unveiled by Silph Road researchers (here) [1]!

For a long time, the understanding has been a Pokestop picks a 2km/5km/10km egg based on an egg-probability distribution, then pick a Pokemon within that distance according to another probability distribution.  For example, the chance of getting a Lapras is $p(Lapras) = p(10km)*p(Lapras|10km)$.  Now there is a much simpler and elegant new theory: eggs are simply determined by one probability distribution - one that is associated with Pokemon alone.  Hatchable Pokemons are assigned to four categories: Common, Uncommon, Rare and Ultra Rare, with hatching probability ratio 8:4:2:1.

The assignment of Pokemons based on their hatch distance and rareness is shown in the table below [2]:

Converting this chart to counts:

RarenessWeight 2km5km 10kmTotal by Rareness (weighted),
Row Sum
Common86102144
Uncommon416153136
Rare214316
Ultra-Rare1113519
Total by Distance (weighted),
Column Sum

11516139315

Imagine there are a total of 315 eggs in a basket, Lapras (ultra-rare) has only one egg, Geodude (common) has eight eggs. Pokestop randomly picks an egg from this basket, distance (egg color) is just a by-product. Then the probability of hatch a particular Pokemon can be calculated based on its category (regardless of its egg distance):
common: 8/315 = 2.54%,
uncommon: 4/315 = 1.27%,
rare: 2/315 = 0.63%,
super rare: 1/315 = 0.32%.

The egg drop probability from a Pokestop can also be explained:
2km: 115/315 = 36.5%,
5km: 161/315 = 51.1%,
10km: 39/315 = 12.4%.
For Lapras, the chance of getting a 10km egg is 12.4%, the chance of that 10km egg being Lapras is: 1/39 = 2.56%.  The overall probability of hatching a Lapras is 1/315 = 0.32%.  This is quite consistent with our previous observations (see my previous Blog entry on hatching).  We can further infer that to hatch a Lapras with a 50% chance, one should hatch 218 eggs, including 27 10km eggs.  To hit an 80% chance, one should hatch 506 eggs, including 62 10km eggs!

Let us check on Gen 2 babies. Babies are all uncommon with a probability of 1.27%, despite of their distances.  So to hatch a particular baby, one needs to hatch 54 eggs (50% chance) or 126 eggs (80% chance) (I hatched Tyrogue with 108 eggs, in agreement).  Pick Tyrogue in particular, one should walk 25 or 59 5km eggs in order to hit 50% and 80% chance, respectively.  Although these many eggs would probably cost you $50 in incubator purchase, it is still way more feasible than hatching a Lapras.

This is indeed a beautiful theory that explains all the mysteries behind eggs! Congratulations to the researchers!

Reference

[1] https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=8&cad=rja&uact=8&ved=0ahUKEwiBroGQzczSAhXGjFQKHZckDJoQqUMIMjAH&url=https%3A%2F%2Fthesilphroad.com%2Fscience%2Fsecret-egg-rarity-tiers-pokemon-go&usg=AFQjCNHhNlqpvW0rLfDNP8byWlLfOhPA5A&sig2=6hWcKtL7eeiMm71pxKNA7w
[2] https://www.reddit.com/r/TheSilphRoad/comments/5ylpzj/chart_of_egg_rarity_divided_by_egg_distance/

Tuesday, February 21, 2017

Gen II - Catch Them All

last updated on April 6, 2017 (Gen II Complete)

Key Gen 2 Milestones:
Apr 6, 2017: Dragon Scale obtained from a spin right after 7-day streak! Complete!
Mar 30, 2017: Up-Grade obtained via 7-day streak.
Mar 21, 2017: Niantic reinstates gauranteed evolution item at 7-day streaks. Counting down to the completion of Gen 2 Pokedex;.
Mar 4, 2017: Tyrogue Hatched! Balboa Park Totodile nest, earn candies for Feraligatr.
Mar 1, 2017: Unown Found!
Feb 26, 2017: Coronado Island Hunt.
Feb 25, 2017: Girafarig Nest and Hunt in Carlsbad.
What are Gen 2s?

Source here:


Babies: Only from Eggs

They are not in wild, the only way to get babies is to hatch.  Even if you got all seven babies during the Christmas event, there is one more baby, Tyrogue, needs to be added to your Pokedex.  So buy incubators and start walking.  The secrete of hatching has been cracked recently (See my other blog entry), Tyrogue and all other babies are as hard/easy to hatch as Chammander, Bulbasaur, Oddish, or Larvitar (with 1.27% chance).  In contrast, Porygon and Lapras are 4 times harder!  So hatching a Tyrogue is definitely can be achieved.  In addition, hatching is an economic way of getting high IV and high CP pokemons, you will have to catch a lot in wild in order to get such pokemons, wasting lots of gas and eventually probably spending more money.  Every 54 eggs give you 50% chance to hatch a Tyrogue, not bad at all.
Tyrogue was finally hatched on Mar 4, 2017.  I walked 760km and hatched 489 eggs right before Gen 2 started (see blog entry), which means it took me 100km and 108 eggs to get Tyrogue.  Based on the "hatch secrete", 36.5% eggs were 2km eggs, to which I always applied the free incubator, the total cost is 108*0.63.5*$0.50/hatch = $34.29.  However, this also covers some other high-IV hatches, such as Mantine, Larvitar, Dratini, Mareep, Gilgar, Aerodactyle, Stander, Phanpy, Wooper, Slugma, etc.

Egg chart here:
Gen 2 starters are not hatchable: Chikorita, Cyndaquil, Tododile, which is actually good news, as they have nests and their removal increases the chance for hatching others.

Rares: Location, Location, Location

Remember our Gen I lesson, some Pokemons only favor coastal areas, so it is important that we visit places such as Coronado Island, La Jolla Cove, Oceanside Pier, etc. in San Diego.  Coastal-friendly ones include Lantun, Mareep, Magcargo, Forrestress, Croconaw, Bayleef, Remoraid, Quilfish, etc. However, many of these can be evolved, e.g., Forrestress can be evolved, where Pinco is not hard to get, Croconaw should be evolved from Totodile, Magcargo from Slugma, Lantun from Chinchou (seems to be missing in the egg chart), Bayleef from Chikorita, so do not be lazy here.  (The water event starts on Mar 22 certainly is a blessing for those who do not live by the beach, best of all, you get a chance to fill that empty Lapras slot!)

Nests: All Starters Have Nests

Make use of Silph Road Nest Atlas, which is pretty accurate now (link here).  I got my Girafarig at the Alga Norte Community Park (maybe 10 spawns per hour), my Sneasel at 4S Ranch Heritage Park (maybe 3 spawns per hour).  Balboa park is an extremely strong Totodile nest, it is mostly easier to catch enough candies to evolve Feraligatr yourselve than counting on encountering one in wild (feraligatr seems to be specific to coastal regions).
Girafarig nest at Algo Norte Community Park.

Balboa Park is an extremely strong Totodile nest.  You should be able to get enough candies for Feraligatr within two hours (hint: do not forget to use the Pinap Berry on weak CP ones to magnify your candy bonus)! There are 2-3 Totodile within nearby sightings constantly, take advantage of it before nest change.  Balboa Park changed into a Gastly nest on the 16th nest change, so when you see a nest of interest, act decisively.


Evolved Forms: Those Require Items are NOT in Wild

My data analysis shows any Gen II that require items (stones, steel case, dragon scale) will not exist in wild. This now has been confirmed by other analyses.  So the only way to get the following eight Pokemons is by obtaining items and evolving them yourself:  Porygon2, Bellossom, Slowking, Steelix, Kingdra, Scizor, Politoed, as well as Sunflora. Umbreon and Espeon are also not in wild.  Blissey and Corbat are in wild, as their evolution does not require items.  Items are rare from Pokestop spins, however, it seems the Day-7 Streak always give an item (happened to me as well) (Update: Evolution items from day-7 Streaks were later removed by Niantic and now reintroduced on March 21!  Without this bonus feature, it was estimated that one evolution items can be expected for every 250 Poke Stop spins, which was terrible for rural player.) So given enough time, these Pokemons are basically in your pocket, if you have played Gen I well.  Make sure get a good IV Eevee, before triggering the Umbreon and Espeon evolution.  (I have got a total of nine items so far, including one 7-day streak item, but I still need dragon scale and Up-grade.)

Items requires for Gen 2 evolution: here
Original Post here

Great news came on Mar 21, 2017!

Items requires for future generations: here (basically only 3 extra sun stones are needed)

April 6 is my 7-day streak day.  With great hope, I spinned and got a King Stone (8:33AM), how disappointing.  This is my 16th items.  I immediately did the math, the probability of an item is either Up-Grade or Dragon Scale is 1/8, the other three items are twice more likely, 1/4 each (based on some statistics on SilphRoad).  So the chance for not getting Dragon Scale 16 times on a roll is  $\left(\frac{7}{8}\right)^{16}=0.12$.  I was not super unlucky, but definitely disappointed.  As I clicked my Pogo+ on my way to work to collect some XP points, the first PokeStop I spin after getting off the highway (this is the spin right after my 7-day spin) was a Dragon Scale!  What a nice way to end my Gen II collection. 


The last wanted item - Dragon Scale was obtained with a drama.

Super Rares: Social Media & Crowd Sourcing

The chance of encountering super rares is very low by your own, so you need to read social media and find spawn information shared by other players or other sources to maximize your chance.  Still remember how hard it was to catch a Lapras, this will apply to some Pokemons in Gen II.

Here is a tentative list of super rares: Meganium (like Venusaur), Typhlosion (like Charizard), Feraligatr (like Blastoise), Togetic (as hard to capture as Dragonite), you might have a better chance to hatch its baby Togepi and walk the candies (well, I have not hatched Togepi after 100 Gen 2 eggs, so not easy either), Ampharos, Jumpluff, Forrestress (better evolve it from Pinco), Hitmontop, Tyranitar (like Dragonite, very rare, seems to favor coastal region, but Lavitar spawns universally, unlike Dratinit.). [hint: Feraligatr can only be found in coast.  Tyranitar can be found in inland.]

Again, I would really recommend evolve Meganium, Typhlosion, Feraligatr, Jumpluff and Tyranitar yourselves, instead of hoping to catch a one in wild.  Not only the chance is low, but also the likelihood of catching both a good IV and high CP one is much more rare and requires many many rare catches.  Is it not too hard to evolve one for them.  Ampharos may be hard given how rare Mareep is, some buddy-walking may be required. You may have a better chance to catch a Hitmontop than hatch two Tyrogue (save one, and use one for evolve).

Region Exclusives: Corsola and Heracross.  Tropical and South American, respectively.  Just visit enough gyms to collect them their silhouette.  The best strategy is to not let them bother you.
Corsola and Heracross were met in gyms.

Unown: Too Hard to Catch

Unowns (a-z) 26 alphabet. After one week of Gen 2, we finally see two spawns in Coronado.  It is much more rare than Lapras, so I would say forget about them, unless you live close to Coronado.  Unown is so rare that there is no point in visiting Coronado just to hit the jackpot, you most likely won't be able to.  We can only hope Niantic will increase its spawn rate or introduce future Unown events.

PS: Unown is super super rare, but there is always someone who wins the lottery.  There have been four Unowns reported so far, one in La Jolla Shores, two in Coronado Island, one in Strand (also Coronado Island).
An Unown was repored at La Jolla Shores on Mar 1, 2017.  Nearly had to get into water to catch.


Enough Unowns have been reported and there is absolutely no pattern in where they spawn.  They show up in places where normally no player would be around!  I do know a guy in Houston, who had an Unown encounter purely by lucky (without using any trackers), the majority of Unown encounters were assisted by trackers (how likely it is you happen to be at a small street at 9:30pm, and that success repeated several times?)  If you really want Unown, the only feasible way is to use your local Tracker, particularly those channels that are specifically created for Unown, so that you get alerts the moment it is broadcast.  Due to the wide spread of possible Unown spwan spots, every second counts in order to arrive at the spot on time.  Even with trackers, Unown hunting is so difficult that every Unown caught will be an unforgettable memory.  People who caught multiple Unowns in multiple cities/continents are very likely doing GPS spoofing, and they use a global Unown tracker (I do not want to name it), just don't let that bother you (sicne not all trackers report Unown letter, even you do not spoof, this tracker is useful to find out what Unown letter is spawned.  Usually spoofers will report the letter minutes after its detection, so that it may save you an unnecessary full trip.).  I forgot to mention that there are 28 Unowns (26 letters plus "!" and "?", only the 26 letters are released in Gen 2).


The Unown family.  Although Unown is only counted as one Pokedex entry, it has 28 difference manifestations.  While most players were praying for just one, some are hunting for all 26 alphabets using a global tracker and GPS spoofing tricks.


A minute after the super super-rare Unown Y was spawn in London, multiple players celebrated their completion of the Unown Gold Medal for collecting all 26 letters!  Do you want to go that far for Unown?

More than a dozen Unown-hunting vehicles showed up at a small street for Unown (I). Residents were probably shocked! 

San Diego Unown map based on 23 spawns.  Except Coronado island is an Unown hot spot, Unown spawn has been spreaded all over San Diego.


Good Candies to Save:

According to a Silph Road post: Togetic, Murkrow, Misdreavus, Aipom, Yanma, Gilgar, Sneasel and Piloswine will have evolutions in Gen IV, so we do need to stock their candies, instead of using all of them for their power-ups.  The same post also mention Porygon2 will have its evolution in Gen IV, so Porygon candies are still needed.

See post here:  Pokemons for Gen 4
Evolution forms of Magneton, Lickitung, Rhydon, Tangela, Electabuzz,
Magmar, Porygon, Togepi, Aipom, Yanma,
Murkrow, Misdreavus, Gilgar, Sneasel, Swinub

Even more forward thinking to future generations, see thread here and reference here.

Region Exclusive

Tauros nearly disappears nowadays.  Farfetch'd is not bad, still availabe in Hongkong.
Screenshot from https://pokemon.appx.hk/ for Farfetch'd and Corosal.

The update region-exclusive map is here: (embedden as well)





Saturday, February 18, 2017

Generation II Early Data Analysis

Last Updated: 2/20/17 8:30am.

Availability Analysis: Wild Pokemons not yet been reported in San Diego:
  • Unown, Corsola.  (Note: Mareep, Pineco and Phanpy was mistakenly filtered out by all trackers.  Fixed in some now).  Corsola now seems to be tropical region exclusive.  Neither Unown nor Entei has been deteced by any trackers.  Unown does exist in wild, apparently all trackers have trouble detecting it.
  • Also not reported:
  • Probably not in game: Delibird, Smeargle, Celebi, Ho-Oh, Lugia, Suicune, Entei, Raikou
  • Babies are not in wild: Cleffa, Igglybuff, Pichu, Togepi, Magby, Elekid, SmoochumTyrogue
  • Regional: Heracross
  • Gen2s that require items in evolution are not available in wild, this incluidng those from Gen1 including Porygon2, Bellossom, Slowking, Steelix, Kingdra, Scizor, Politoed, as well as Sunflora from Gen2.  Despite people have shown screenshot, I have not read evidence that these were caught in wild (unless there is a bug in multiple trackers). Blissey and Crobat are availabe in wild, because their evolutions do not require stone. We have not seen Umbreon and Espeon in wild in San Diego.  We have data for 10523 rare spawns and these were not observed. So I can say for sure this is the case!
Coronado Spawn Rareness Analysis

Coronado (including Strand) spawns during 2/18/17 2:30am-2/20 7:00:pm (52 hours), Inland data are collected from UTC, Rancho Penasquitos and Zip code 92116.

Spawns in San Diego:
Evolution Level 1. Low counts for Mareep and Phanpy were due to tracker filtering.

Evolution Level 2-3. Notice Girafarig, Ampharos and Forrestress are more rare than Feraligatr, Jumpluff and Meganium. (Do trackers filter them?)

Rareness for Coronado Only:
Evolution Level 1

Evolution Level 2-3

Spawn Location Preference Analysis: Coronado versus Inland
Note: Coronado data includes some common ones but high IV, e.g., Hoothoot, Houndour, ignore those.
Comparison between Coronado Data vs Inland Data


Thursday, February 16, 2017

My Game of Pokemon GO: Stage ? - Region Exclusives

This is the last blog entry of my Pokemon GO Gen I series.  Gen II is released today with new sets of silhouette, which is why I am rushing to backup my Gen I memory data onto this disk space.

Tauros is exclusive to North America, Farfetch'd to Asia, Kangaskhan to Australia/New Zealand, and Mr Mime to Europe.  Except Tauros, the rest three certainly are out of reach (can no longer be hatched from eggs either).  The best I could do was to meet them in gyms, which was mistakenly counted as a failed encounter in the game.  Nevertheless seeing a Pokemon in a gym adds a clickable silhouette into your Pokedex.  Collecting all three silhouettes could be a practical relaxed definition for completing of the global Pokedex.

My collection of the regional silhouettes.  Mr Mime was seen in a gym near my house;  Farfetch'd in San Diego Airport on my trip back from Cancun;  Kangaskhan at Coronado Island.

Resources Saved for Future Intercontinental Trips

This section is just for my own bookmarking purpose.

Region-exclusive nests: https://thesilphroad.com/atlas, however, not well maintained.

Kangaskhan in Sydney:
However, Kangaskhan was declared to be as common as Pidgey and were filtered out from the map.  The explanation for this was humorous
Q: Hello, this is Pidgey. Why am I not on the map? I demand a refund #PidgeyLivesMatter.A: Hello Pidgey, THERE ARE SO MANY OF YOU, so to keep your trainers sane, we filter you out. Bellsprout, Caterpie, Clefairy, Ekans, Golbat, Goldeen, Horsea, Kangaskhan, Krabby, Nidoran♀, Nidoran♂, Oddish, Paras, Pidgeotto, Pinsir, Poliwag, Psyduck, Rattata, Sandshrew, Slowpoke, Spearow, Staryu, Venonat, Weedle and Zubat are also not on the map but they didn't complain, did they? #AllMonsAreEqualButSomeMonsAreMoreEqualThanOthers.


Farfetch'd:
It was mentioned that Farfetch'd spawn frequently nearer Taipei 101.

Mr Mime: