Hōʻike HN: Hopalong Attractor. He kuʻuna kahiko me kahi hiʻohiʻona hou ma 3D

Mai Pixels a hiki i nā Mamana: E nānā hou i ka Hopalong Attractor

I loko o ke ao o ka hoʻonaʻauao ʻana, he liʻiliʻi nā ʻōnaehana i loaʻa ka nani maʻalahi a me ka paʻakikī o ka Hopalong Attractor. Ua wehewehe mua ʻia e Barry Martin i nā makahiki 1980, ʻo kēia algorithm kahi mea nui o nā kiʻi kamepiula mua, i hoʻohana pinepine ʻia e hana i nā kiʻi kupanaha, like me nā galaxy mai kahi ʻano maʻalahi hoʻopunipuni. No nā makahiki he nui, mahalo mākou i kēia mau fractals i ko lākou nani ʻelua. Akā he aha ka hopena ke hele mākou ma waho o ka mokulele palahalaha a kono i ke kolu o ke ana i loko o ka hoohalike? ʻO kā mākou papahana "Show HN" hou e hana like me ia, e hanu ana i ke ola hou i loko o kēia moʻomeheu kahiko ma o ka ʻimi ʻana i ka Hopalong Attractor mai kahi hiʻohiʻona hou, volumetric.

Ke wehe ʻana i ka Classic: Pehea e hana ai ka mea hoʻohihi

Ma kona puʻuwai, ʻo ka Hopalong Attractor maʻamau he hana hoʻomau. Loaʻa i kahi helu hoʻomaka (x, y) a, ma o ke ʻano o nā hana makemakika, lele ia i kahi wahi hou. ʻO ke kumuhana, hāʻawi pinepine ʻia penei:

• x_n+1 = y_n - hōʻailona(x_n) * sqrt(|b * x_n - c|)
• y_n+1 = a - x_n

...hana i ke ala o nā kiko, i ka wā i hoʻolālā ʻia ai ma luna o nā tausani o ka hoʻololi ʻana, ʻaʻole e hoʻohuli i kahi kiko hoʻokahi akā i kahi hale nani a paʻakikī. ʻO nā ʻāpana a, b, a me c ke hana ma ke ʻano he "DNA" o ka mea hoihoi, me nā hoʻololi minuke i hopena i nā hopena ʻike ʻokoʻa ʻē aʻe, mai nā apo orbital maʻalahi a hiki i nā puʻupuʻu e like me ke ao. He hōʻike ikaika ia o ka hiki ʻana mai o ka hoʻonohonoho paʻakikī mai nā lula maʻalahi a me ka hoʻoholo.

He Mana Hou o ka ʻIke: Ka Hoʻololi 3D

ʻOi aku ka lele mai 2D a i 3D ma mua o ka hoʻopunipuni ʻike wale; ʻo ia ka hoʻoponopono hou ʻana o ka ʻōnaehana. Ma kahi o ka hoʻopaʻa ʻana i ka huakaʻi o ka lae i kahi kāwele palahalaha, ua hoʻokomo mākou i ke kolu o ke ana, z, e ʻae ana i ke kiko e ʻōpuni ma waena o ka lewa. Loaʻa kēia ma ka hoʻonui ʻana i ka hoʻonohonoho hoʻohālikelike, e hana ana i kahi puka manaʻo kahi e hoʻopili ai ka z-coordinate i nā kūlana x a me y aʻe, a me ka hope. ʻAʻole ʻo ka hopena he palahalaha e like me ka galaxy smear, akā he ʻano hoʻonaninani ʻekolu-dimensional e hiki ai iā ʻoe ke ʻōpuni a lele i loko. Loaʻa ka hohonu, ke ʻano, a me ke ʻano o ke kino i hiki ʻole i ka hoʻokumu mua ʻana. Ua like ia me ka hoʻohālikelike ʻana i ke kiʻi o ka nebula me kahi moku lewa e lele ana ma ia wahi.

"ʻO ka ʻike ʻana i ka Hopalong Attractor ma 3D ʻaʻole ia e pili ana i ka hoʻomaʻamaʻa ʻana.

Mai nā Orbit Chaotic a i nā Pūnaehana Cohesive: Ka Hoʻohui Mewayz

Kuhi nui kēia papahana me kā mākou hana ma Mewayz. Ma ka ʻaoʻao, ʻaʻohe mea liʻiliʻi o ka hula chaotic o kahi helu hoʻokahi ma hope o ka algorithm Hopalong me kahi ʻōnaehana ʻoihana modular. Akā, e nānā pono, a ʻike ʻia ka like. E like me ka hoʻokumu ʻia ʻana o nā lula makemakika i ʻike ʻia i kahi hoʻolālā paʻa a nani, ʻo ka ʻoihana he ʻōnaehana paʻakikī kahi e hiki ai i nā hana pilikino ke helu ʻia, nā helu ʻikepili, a me nā pilina hui. ʻO ka mana o kahi ʻōnaehana e like me Mewayz ʻo ia kona hiki ke hana ma ke ʻano he mea hoʻowalewale, e hāʻawi ana i kahi papa hana i kūkulu ʻia - kahi ʻano o ka gravity hoʻonohonoho - e huki i kēia mau mea ʻokoʻa i loko o kahi hui pū, kūpono, a ʻike ʻia. Ma ka hoʻoneʻe ʻana i ka Hopalong i 3D, ua loaʻa iā mākou ka ʻike piha o kona ʻano; like, hoʻoneʻe ʻo Mewayz i nā hana pāʻoihana mai kahi huikau 2D o nā pāpalapala a me nā leka uila i kahi ʻāina 3D akaka kahi i loaʻa i nā mea āpau kona wahi a me kona kumu.

Ka Hoʻohiwahiwa Paʻa ʻana o ka Paʻakikī e kū mai ana

He mea hoʻomanaʻo maikaʻi ka hiʻohiʻona 3D hou ma ka Hopalong Attractor e hiki i nā ala hele maikaʻi ke alakaʻi i nā ʻike hou ke nānā ʻia mai kahi kihi ʻokoʻa. Hōʻike ia i kahi loina a mākou e paʻa ai ma Mewayz: ʻaʻole pono ka paʻakikī. Ma ke kiʻi makemakika a ma ka ʻoihana paha, hiki i ke kaʻina hana kūpono ke hoʻololi i ka haunaele i ka mālamalama, e hōʻike ana i nā hiʻohiʻona nani i hūnā ʻia i loko. Ke kono nei mākou iā ʻoe ʻaʻole e nānā wale i kēia mau hana 3D hou, akā e makaʻala iā lākou, e ʻike i ke ʻano o ka hana ʻana o kēlā me kēia hoʻololi ʻana i ke ʻano hou o ke ʻano, a e noʻonoʻo i ke ʻano o ka lawe ʻana i kahi ʻano hou o ka hui i kāu hana ponoʻī e hōʻike i kahi ala maikaʻi a maikaʻi o ka hana.

Nīnau pinepine

Mai nā Piki a i nā Mamana: E nānā hou ana i ka Hopalong Attractor

I loko o ke ao o ka hoʻonaʻauao ʻana, he liʻiliʻi nā ʻōnaehana i loaʻa ka nani maʻalahi a me ka paʻakikī o ka Hopalong Attractor. Ua wehewehe mua ʻia e Barry Martin i nā makahiki 1980, ʻo kēia algorithm kahi mea nui o nā kiʻi kamepiula mua, i hoʻohana pinepine ʻia e hana i nā kiʻi kupanaha, like me nā galaxy mai kahi ʻano maʻalahi hoʻopunipuni. No nā makahiki he nui, mahalo mākou i kēia mau fractals i ko lākou nani ʻelua. Akā he aha ka hopena ke hele mākou ma waho o ka mokulele palahalaha a kono i ke kolu o ke ana i loko o ka hoohalike? ʻO kā mākou papahana "Show HN" hou e hana like me ia, e hanu ana i ke ola hou i loko o kēia moʻomeheu kahiko ma o ka ʻimi ʻana i ka Hopalong Attractor mai kahi hiʻohiʻona hou, volumetric.

Ke wehe ʻana i ka Classic: Pehea e hana ai ka mea hoʻohihi

Ma kona puʻuwai, ʻo ka Hopalong Attractor maʻamau he hana hoʻomau. Loaʻa i kahi helu hoʻomaka (x, y) a, ma o ke ʻano o nā hana makemakika, lele ia i kahi wahi hou. ʻO ke kumuhana, hāʻawi pinepine ʻia penei:

He Mana Hou o ka ʻIke: Ka Hoʻololi 3D

ʻOi aku ka lele mai 2D a i 3D ma mua o ka hoʻopunipuni ʻike wale; ʻo ia ka hoʻoponopono hou ʻana o ka ʻōnaehana. Ma kahi o ka hoʻopaʻa ʻana i ka huakaʻi o ka lae i kahi kāwele palahalaha, ua hoʻokomo mākou i ke kolu o ke ana, z, e ʻae ana i ke kiko e ʻōpuni ma waena o ka lewa. Loaʻa kēia ma ka hoʻonui ʻana i ka hoʻonohonoho hoʻohālikelike, e hana ana i kahi puka manaʻo kahi e hoʻopili ai ka z-coordinate i nā kūlana x a me y aʻe, a me ka hope. ʻAʻole ʻo ka hopena he palahalaha e like me ka galaxy smear, akā he ʻano hoʻonaninani ʻekolu-dimensional e hiki ai iā ʻoe ke ʻōpuni a lele i loko. Loaʻa ka hohonu, ke ʻano, a me ke ʻano o ke kino i hiki ʻole i ka hoʻokumu mua ʻana. Ua like ia me ka hoʻohālikelike ʻana i ke kiʻi o ka nebula me kahi moku lewa e lele ana ma ia wahi.

Mai nā Orbit Chaotic a i nā Pūnaehana Cohesive: Ka Hoʻohui Mewayz

Kuhi nui kēia papahana me kā mākou hana ma Mewayz. Ma ka ʻaoʻao, ʻaʻohe mea liʻiliʻi o ka hula chaotic o kahi helu hoʻokahi ma hope o ka algorithm Hopalong me kahi ʻōnaehana ʻoihana modular. Akā, e nānā pono, a ʻike ʻia ka like. E like me ka hoʻokumu ʻia ʻana o nā lula makemakika i ʻike ʻia i kahi hoʻolālā paʻa a nani, ʻo ka ʻoihana he ʻōnaehana paʻakikī kahi e hiki ai i nā hana pilikino ke helu ʻia, nā helu ʻikepili, a me nā pilina hui. ʻO ka mana o kahi ʻōnaehana e like me Mewayz ʻo ia kona hiki ke hana ma ke ʻano he mea hoʻowalewale, e hāʻawi ana i kahi papa hana i kūkulu ʻia - kahi ʻano o ka gravity hoʻonohonoho - e huki i kēia mau mea ʻokoʻa i loko o kahi hui pū, kūpono, a ʻike ʻia. Ma ka hoʻoneʻe ʻana i ka Hopalong i 3D, ua loaʻa iā mākou ka ʻike piha o kona ʻano; like, hoʻoneʻe ʻo Mewayz i nā hana pāʻoihana mai kahi huikau 2D o nā pāpalapala a me nā leka uila i kahi ʻāina 3D akaka kahi i loaʻa i nā mea āpau kona wahi a me kona kumu.

Ka Hoʻohiwahiwa Paʻa ʻana o ka Paʻakikī e kū mai ana

He mea hoʻomanaʻo maikaʻi ka hiʻohiʻona 3D hou ma ka Hopalong Attractor e hiki i nā ala hele maikaʻi ke alakaʻi i nā ʻike hou ke nānā ʻia mai kahi kihi ʻokoʻa. Hōʻike ia i kahi loina a mākou e paʻa ai ma Mewayz: ʻaʻole pono ka paʻakikī. Ma ke kiʻi makemakika a ma ka ʻoihana paha, hiki i ke kaʻina hana kūpono ke hoʻololi i ka haunaele i ka mālamalama, e hōʻike ana i nā hiʻohiʻona nani i hūnā ʻia i loko. Ke kono nei mākou iā ʻoe ʻaʻole e nānā wale i kēia mau hana 3D hou, akā e makaʻala iā lākou, e ʻike i ke ʻano o ka hana ʻana o kēlā me kēia hoʻololi ʻana i ke ʻano hou o ke ʻano, a e noʻonoʻo i ke ʻano o ka lawe ʻana i kahi ʻano hou o ka hui i kāu hana ponoʻī e hōʻike i kahi ala maikaʻi a maikaʻi o ka hana.