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Challenges Is it part of the mandelbrot set?

Python 3.8, 57 bytes -2 bytes (2025-04-02) def m(c): for _ in range(16):(z:=c)*z+c return abs(z)<2 Try it online (59 byte version) Returns False if c (a complex number) is not part o...

posted 3d ago by CrSb0001‭ · edited 1d ago by CrSb0001‭

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#2: Post edited by

CrSb0001‭ · 2025-04-02T14:37:24Z (1 day ago)
2 byte save on my current smallest submission, 21 bytes saved from the one that takes input from STDIN.

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~~# Python 3.8, 59 bytes~~
```python
def m(c):
~~z=c~~
~~for _ in range(16):z=z*z+c~~
return abs(z)<2
```
~~[Try it online]~~
Returns `False` if `c` (a complex number) is not part of the Mandelbrot set after 16 iterations, `True` otherwise.
Uses @ArpadHorvath's observation that if `abs(z)` is ever greater than 2, it will always be greater than 2 in the iterations following that.
---
~~If we require input from STDIN using the `input()` function, then I have an equivalent 85 byte program:~~
```
b=complex(*map(float,input().split()))
~~z=b~~
~~for _ in range(16):z=z*z+b~~
print(abs(z)<2)
```
Should be pretty self explanatory as it's basically the exact same thing as the function I have at the top.
[Try it online]:https://tio.run/##K6gsycjPM7YoKPr/PyU1TSFXI1nTikuhyjaZSyEtv0ghXiEzT6EoMS89VcPQTNOqyrZKq0obKFeUWlJalKeQmFSsUaVpY/T/PwA

# Python 3.8, 57 bytes
<i>-2 bytes (`2025-04-02`)</i>
```python
def m(c):
for _ in range(16):(z:=c)*z+c
return abs(z)<2
```
[Try it online] (59 byte version)
---
Returns `False` if `c` (a complex number) is not part of the Mandelbrot set after 16 iterations, `True` otherwise.
Uses @ArpadHorvath's observation that if `abs(z)` is ever greater than 2, it will always be greater than 2 in the iterations following that.
---
If we require input from STDIN using the `input()` function, then I have an equivalent <strike>85</strike> <strike>84</strike> 64 byte program:
```
b=complex(input())
for _ in range(16):(z:=b)*z+b
print(abs(z)<2)
```
Should be pretty self explanatory as it's basically the exact same thing as the function I have at the top.
Takes input as a regular Python complex number, which is how I managed to save another 20 bytes aside from writing the loop using the walrus operator `:=`.
[Try it online]:https://tio.run/##K6gsycjPM7YoKPr/PyU1TSFXI1nTikuhyjaZSyEtv0ghXiEzT6EoMS89VcPQTNOqyrZKq0obKFeUWlJalKeQmFSsUaVpY/T/PwA

#1: Initial revision by

CrSb0001‭ · 2025-03-31T17:51:45Z (3 days ago)

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# Python 3.8, 59 bytes

```python
def m(c):
 z=c
 for _ in range(16):z=z*z+c
 return abs(z)<2
```
[Try it online]

Returns `False` if `c` (a complex number) is not part of the Mandelbrot set after 16 iterations, `True` otherwise.

Uses @ArpadHorvath's observation that if `abs(z)` is ever greater than 2, it will always be greater than 2 in the iterations following that.

---

If we require input from STDIN using the `input()` function, then I have an equivalent 85 byte program:

```
b=complex(*map(float,input().split()))
z=b
for _ in range(16):z=z*z+b
print(abs(z)<2)
```
Should be pretty self explanatory as it's basically the exact same thing as the function I have at the top.

[Try it online]:https://tio.run/##K6gsycjPM7YoKPr/PyU1TSFXI1nTikuhyjaZSyEtv0ghXiEzT6EoMS89VcPQTNOqyrZKq0obKFeUWlJalKeQmFSsUaVpY/T/PwA

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