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Note 7 - Real Estate - Real Estate Disclosure (Details) - USD ($) | 12 Months Ended
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Dec. 31, 2020 | Dec. 31, 2019
Net Realizable Value at beginning of period | $ 48,270,000 | $ 36,201,270
Increase (decrease) in net realizable value | (9,220,000) | 12,068,730
Net Realizable Value on December 31, | 39,050,000 | 48,270,000
Cortlandt Manor Medical Center [Member] |  |
Increase (decrease) in net realizable value | (3,820,000) | 2,010,000
Flowerfield Properties, Inc. [Member] |  |
Increase (decrease) in net realizable value | $ (5,400,000) | $ 10,058,730

X
- Definition Amount of increase (decrease) before accumulated depreciation of investments in land and buildings held for sale, excluding real estate considered to be inventory of the entity. + References No definition available. + Details
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Namespace Prefix: | gyro_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Definition Carrying amount as of the balance sheet date of investments in land and buildings held for sale, excluding real estate considered to be inventory of the entity. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 944 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.7-03.1(f)) -URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910 + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

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- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_LongLivedAssetsHeldForSaleByAssetTypeAxis=gyro_FlowerfieldPropertiesIncMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |