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Note:This journal is a direct continuation of the previous journal Beware, Hexics released
And now, Ladies and Gentlemen, my dear friend
, also has released the formula Heptic parameterspace3 and the related Heptic Julia3. It is included in his sp3 folder. That folder is included in this zip
so it’s again time to upgrade the sp3 folder.
Heptics:
z -> z^7 + 7/5[ab + ac + ad + ae + bc + bd + be + cd + ce + de - (a + b + c + d + e)^2]z^5 - 7/4[abc + abd + abe + acd + ace + ade + bcd + bce + bde + cde - (ab + ac + ad + ae + bc + bd + be + cd + ce + de)(a + b + c + d + e)]z^4 + 7/3[abcd + abce + abde + acde + acde - (abc + abd + abe + acd + ace + ade + bcd + bce + bde + cde)(a + b + c + d + e)]z^3 - 7/2[abcde - (abcd + abce + abde + acde + acde)(a + b + c + d + e)]z^2 - 7abcde(a + b + c + d + e)z + f, critical points, z = a, z = b, z = c, z = d, z = e and z = -(a + b + c +d + e).
Having six complex parameters (a, b, c, d, e, f) the heptic parameter space is a twelve dimensional hyperspace
The set of (a, b, c, d, e, f) for which the critical point z = a has a bounded orbit is called M1. The set of (a, b, c, d, e, f) for which the critical point z = b has a bounded orbit is called M2. The set of (a, b, c, d, e, f) for which the critical point z = c has a bounded orbit is called M3. The set of (a, b, c, d, e, f) for which the critical point z = d has a bounded orbit is called M4. The set of (a, b, c, d, e, f) for which the critical point z = e has a bounded orbit is called M5. And finally the set of (a, b, c, d, e, f) for which the critical point z = -(a + b + c + d + e) has a bounded orbit is called M6. The set of (a, b, c, d, e, f) belonging to ALL sets (M1, M2, M3, M4, M5, M6) is called Heptic Connectedness Locus (HCL).
Puuuh
In this type of parameterizing new phenomena occur for every additional degree. However the most additional new things occurs when you increase to an odd degree (cubics, pentics heptics, etc). In heptics there are many interesting phenomena which hopefully will be demonstrated here by me (and maybe you)
So play and have fun, glide carefully along the non plotted axis’, and don’t get lost among the 66 perpendicular systems of 2D slices
And now, Ladies and Gentlemen, my dear friend
, also has released the formula Heptic parameterspace3 and the related Heptic Julia3. It is included in his sp3 folder. That folder is included in this zipso it’s again time to upgrade the sp3 folder.
Heptics:
z -> z^7 + 7/5[ab + ac + ad + ae + bc + bd + be + cd + ce + de - (a + b + c + d + e)^2]z^5 - 7/4[abc + abd + abe + acd + ace + ade + bcd + bce + bde + cde - (ab + ac + ad + ae + bc + bd + be + cd + ce + de)(a + b + c + d + e)]z^4 + 7/3[abcd + abce + abde + acde + acde - (abc + abd + abe + acd + ace + ade + bcd + bce + bde + cde)(a + b + c + d + e)]z^3 - 7/2[abcde - (abcd + abce + abde + acde + acde)(a + b + c + d + e)]z^2 - 7abcde(a + b + c + d + e)z + f, critical points, z = a, z = b, z = c, z = d, z = e and z = -(a + b + c +d + e).
Having six complex parameters (a, b, c, d, e, f) the heptic parameter space is a twelve dimensional hyperspace
The set of (a, b, c, d, e, f) for which the critical point z = a has a bounded orbit is called M1. The set of (a, b, c, d, e, f) for which the critical point z = b has a bounded orbit is called M2. The set of (a, b, c, d, e, f) for which the critical point z = c has a bounded orbit is called M3. The set of (a, b, c, d, e, f) for which the critical point z = d has a bounded orbit is called M4. The set of (a, b, c, d, e, f) for which the critical point z = e has a bounded orbit is called M5. And finally the set of (a, b, c, d, e, f) for which the critical point z = -(a + b + c + d + e) has a bounded orbit is called M6. The set of (a, b, c, d, e, f) belonging to ALL sets (M1, M2, M3, M4, M5, M6) is called Heptic Connectedness Locus (HCL).Puuuh
In this type of parameterizing new phenomena occur for every additional degree. However the most additional new things occurs when you increase to an odd degree (cubics, pentics heptics, etc). In heptics there are many interesting phenomena which hopefully will be demonstrated here by me (and maybe you)
So play and have fun, glide carefully along the non plotted axis’, and don’t get lost among the 66 perpendicular systems of 2D slices
A Christmas Greeting from Sweden
As a Christmas greeting from Sweden I will promote a YouTube channel by the nature filmer and photographer, Jonna Jinton. The link goes to her channel. Go and see the 15 minutes introduction video in full screen, the image below from the beginning of the video, The scenarios are a mix from both midwinter, midsummer, and other seasons. The soundtrack is as beautiful as the scenarios, and Jonna speaks in English with a relaxing voice. I myself live in the very south of Sweden about more than thousand kilometers south from the area where Jonna and her man and dog lives, the conditions of life being quite different. Here the sun shines for about 7 hours at midwinter. Just click the introduction video, put it in full view and enjoy :snowflake: :santa: :snowflake:
How I Became Interested in Fractals
This journal ought to have been written and published for at least a decade ago The year 1987 it was an India festival in Sweden. At that time, besides my work (I was a shift worker), I was studying Sanskrit at the university of Gothenburg. My special interest was the way they wrote grammar in ancient India about 500 BC. An evening at the late autumn I was sitting with some friends in Stockholm, the capital of Sweden, and watched a TV program about Indian dance. At the end of the program, the speaker talked a little of the theory behind the dance. I don't remember what he said in details, but it was something about how the god of dance, Shiva, transformed order into chaos and chaos into order. Then a map was shown of the coast line of Great Britain and the speaker quite naturally went into that "today the mathematicians has found that there is an order behind the irregular". The subject was the new science about chaos and complexity. Both Mandelbrot and
A special flashmob
This is journal I ought to have written and published for at least one year ago. But as we say in Sweden, ”better late then never”. So first, what is a flashmob? ”A flash mob (or flashmob) is a group of people who assemble suddenly in a public place, perform for a brief time, then quickly disperse, often for the purposes of entertainment, satire, and artistic expression. Flash mobs may be organized via telecommunications, social media, or viral emails.” Quotation from Wikipedia. Back to August, 2021, when there still was some Covid restrictions in Sweden, a group around the Swedish musician and producer Christoffer Lundquist started to perform some flashmobs at some squares in Malmo (the third biggest city in Sweden) and Lund (Sweden's Oxford) at the very south of Sweden. He had just produced a new song that was a protest against the Covid restrictions we had at that time. Now remember that those restrictions were the most liberal in the western world. Yet we were less affected by
The Dreams of World Economic Forum
Hi everyone, Yuval Noah Harari is the one of the advisors to the founder and chair man of World Economic Forumm (WEF) Klaus Schwab.You can read about him (Harari) at Wikipedia.There is an interesting channel at BITCHUTE, HighImpactFlixwho has uploaded 2 videos, 9 minutes and 14 minutes where Harari dreams trans humanistic dreams, Something REALLY BAD is About to Fundamentally Change Humanity - (Pt 1) Some quotes from the video: "What should we do with all these useless people" (Already discussed, due to the fact that about 90 percent of the today's employments will disappear as a consequence of the fourth industrial revolution.) "People could look back in a hundred years and identify the corona epidemic as a moment when a new regime of surveillance took over, especially surveillance under the skin". (You probably know that you may have the vaccine passport as a chip under your skin. The proposals of vaccine passorts where already there in EU as a ”health passport”. Social
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